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Tutors Answer Your Questions about Travel Word Problems (FREE)
Question 241448: Two cars leave town at the same time going in the same direction. One travels at 45 mph and the other travels at 68 mph. In how many hours will they be 138 miles apart.
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(26284)   (Show Source):
You can put this solution on YOUR website!Two cars leave town at the same time going in the same direction. One travels at 45 mph and the other travels at 68 mph. In how many hours will they be 138 miles apart.
---------------------
1st car:
rate = 45 mph ; time = x hrs ; distance = 45x miles
-------------------
2nd car :
rate = 68 mph ; time = x hrs ; distance = 68x miles
---------------------------
Equation:
distance 2 - distance 1 = 138 miles
68x - 45x = 138
23x = 138
x = 6 hours
======================
Cheers,
Stan H.
Answer by Alan3354(6089)  (Show Source):
You can put this solution on YOUR website!Two cars leave town at the same time going in the same direction. One travels at 45 mph and the other travels at 68 mph. In how many hours will they be 138 miles apart.
------------
They're separating at 23 mph (68 - 45)
138/23 = 6 hours
Question 241293: what is
Trains A and B are traveling in the same direction on parallel tracks. train a is traveling at 100 miles per hour and train b is traveling at 125 miles per hour. Train A passes a station at 2:10 A.M If train B passes the same station at 2:22 am, at what time will train b catch up to train A?
When will train B catch up with train A?
Answer by checkley77(7068) (Show Source):
You can put this solution on YOUR website!100t=125(t-12/60)
100t=125t-.2*125
100t-125t=-25
25t=25
t=25/25
t=1 hour after train leave they will meet.
Proof:
100*1=125(1-.2
100=125*.8
100=100
Question 241179: if jake runs 18 miles in 3 hour, what was his speed
Answer by rfer(2688) (Show Source):
Question 241089: Rachel allows herself 1 hr to reach a sales appointment 50 miles away. After she has driven 30 miles, she realizes that she must increase her speed by 15 mph in order to get there on time. What was her speed for the first 30 miles?
Answer by ankor@dixie-net.com(6693)  (Show Source):
You can put this solution on YOUR website!Rachel allows herself 1 hr to reach a sales appointment 50 miles away.
After she has driven 30 miles, she realizes that she must increase her speed by 15 mph in order to get there on time.
What was her speed for the first 30 miles?
:
Let s = speed for the 1st 30 mi
then
(s+15) = speed for the last 20 miles
:
Write a time equation: Time = 
:
1st 30 mi time + last 20 mi time = 1 hour
 +  = 1
Multiply equation by s(s+15), results
30(s+15) + 20s = s(s+15)
:
30s + 450 + 20s = s^2 + 15s
:
50s + 450 = s^2 + 15s
Arrange as a quadratic equation
0 = s^2 + 15s - 50s - 450
:
s^2 - 35s - 450 = 0
Factor
(s - 45)(s + 10) = 0
positive solution
s = 45 mph for the 1st 30 mi
then
45 + 15 = 60 mph for the last 20 mi
;
:
See if that adds up
 +  =
 +  = 1 hr
Question 241120: if earth had an high way and a car can go 55 miles/hr and leave november 10 when would you arrive
Answer by Alan3354(6089) (Show Source):
Question 241090: In a stream, the amount S of salt carried varies directly as the sixth power of the speed V of the stream.
Answer by nyc_function(260)  (Show Source):
You can put this solution on YOUR website!This question is not complete. What is the rest of the problem?
=================================================================
I got your reply. Yes, it does not help. The question is requesting an equation and nothing more.
QUESTION:
In a stream, the amount S of salt carried varies directly as the sixth power of the speed V of the stream.
The equation is:
S = k(V^6)
Question 241034: a driver who drives at a speed of r mph for t hr will travel a distance of d mi given by d= rt mi. How far will a driver travel at a speed of 61 mph for 5 hrs? What is the distance traveled?
Answer by checkley77(7068) (Show Source):
Question 241087: Bob, driving a new Ford, travels 330 miles in the same amount of time it takes John, driving an old Chevy and traveling 10 miles per hour faster, to travel 390 miles. How fast is John driving?
Answer by nyc_function(260) (Show Source):
Question 240990: The problem is: Two planes are 6000 miles apart, and their speeds differ by 200 miles per hour. They travel toward each other and meet in 5 hours. Find the speed of the slower plane.
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website! Two planes are 6000 miles apart, and their speeds differ by 200 miles per hour.
They travel toward each other and meet in 5 hours.
Find the speed of the slower plane.
:
let s = speed of the slower speed
then
(s+200) = speed of the faster
:
Write a distance equation: dist = time * speed
:
slow plane dist + fast plane dist = 6000mi
5s + 5(s+200) = 6000
5s + 5s + 1000 = 6000
10s = 6000 - 1000
10s = 5000
s = 500 mph is the slow speed
;
:
Check solution (fast speed plane = 700 mph
5(500) + 5(700) =
2500 + 3500 = 6000
Question 241020: a man travels 100 miles North from point A and than 200 miles west how far from point A is the man?
Answer by unlockmath(117)  (Show Source):
You can put this solution on YOUR website!Hello,
We need to assume he travels directly west, then we can use the
C^2=A^2+B^2 formula. This is used to find the hypotenuse of a right triangle.
So plug in the numbers which will look like this:
c^2=100^2+200^2 Do the math will give us: (Note c^2 represents the diagonal)
c^2=10000+40000 Add like terms gives us:
c^2=50000 Now square root both sides gives us:
c=223.61 miles (Rounded off to the nearest hundredth)
RJ Toftness
www.math-unlock.com
Question 240734: A remote control car races straight down the street at 26 miles per hour. Two hours later, a second remote control car races straight down the same street at 52 miles per hour in pursuit of the first car. From the moment the first car started, how many hours will it take the second car to catch up to the first?
Answer by Alan3354(6089) (Show Source):
You can put this solution on YOUR website! A remote control car races straight down the street at 26 miles per hour. Two hours later, a second remote control car races straight down the same street at 52 miles per hour in pursuit of the first car. From the moment the first car started, how many hours will it take the second car to catch up to the first?
------------------
Car 1 is 52 miles away (26 mph * 2hr)
Car 2 gains on Car 1 at 26 mph (52 - 26)
52/26 = 2 hours to overtake Car 1
--> 4 hours from the time Car 1 passed
Question 240857: A plane with the wind traveled 855 miles at 143mph. flying against the wind at the same rate of speed it traveled 575 miles. Find the rate of the wind and the time it took to travel in either direction.
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!A plane with the wind traveled 855 miles at 143mph.
flying against the wind at the same rate of speed it traveled 575 miles.
Find the rate of the wind and the time it took to travel in either direction.
:
Let w = rate of the wind
then
(143-w) = plane speed against the wind
and
(143+w) = plane speed with the wind:
:
Assume that the time for each trip was equal; write a time equation: Time = dist/speed
:
 = 
Cross multiply
575(143+w) = 855(143-w)
;
82225 + 575w = 122265 - 855w
:
575w + 855w = 122265 - 82225
:
1430w = 40040
w = 
w = 28 mph is the rate of the wind
:
:
Find the time:
 = 5 hrs
Check solution:
 = 5 hrs also
Question 240922: If a truck traveling to town b from town a, going at a speed of 45km an hour and another truck traveling to town a from town b, is going at a speed of 54km an hour and 20 minutes later they meet each other. How far is the distance between town a and town b?
Answer by stanbon(26284) (Show Source):
You can put this solution on YOUR website!If a truck traveling to town b from town a, going at a speed of 45km an hour and another truck traveling to town a from town b, is going at a speed of 54km an hour and 20 minutes later they meet each other. How far is the distance between town a and town b?
----------------------------
a to b DATA:
rate = 45 km/h ; time = 4/3 hrs; distance = r*t = (4/3)45 = 60 km
-----------------------------
b to a DATA:
rate = 54 km/h ; time = 4/3 hrs; distance = r*t = (4/3)54 = 72 km
-----------------------------
Distance from a to b = 60 + 72 = 132 km
============================================
Cheers,
Stan H.
Question 240800: A train leaves a station and travels north at 50km/hr. Three hours later, a second train leaves on a parallel track and travels north at 90km/hr. How far from the station will they meet?
Answer by Alan3354(6089) (Show Source):
You can put this solution on YOUR website!A train leaves a station and travels north at 50km/hr. Three hours later, a second train leaves on a parallel track and travels north at 90km/hr. How far from the station will they meet?
---------------------
In 3 hours, the 1st train is 150 km away (50*3)
The 2nd train gains on it at 40 kph (90 - 50)
To overtake it will take 3.75 hours (150/40)
3.75 hr * 90 km/hr = 337.5 km from the station
-------------
There are other ways to work this that are more complicated and take more steps and more time.
Do them like this.
Question 240529: The capacities of two trucks are 3 tons and 4 tons respectively. If the smaller truck makes 18 more trips than the larger, it can deliver 12 more tons of freight than the larger. How many trips does each truck make?
Let x represent the number of trips that the larger truck makes. Which of the following equations could be used to solve the problem?
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!The capacities of two trucks are 3 tons and 4 tons respectively.
If the smaller truck makes 18 more trips than the larger, it can deliver 12 more tons of freight than the larger.
How many trips does each truck make?
Let x represent the number of trips that the larger truck makes.
:
x = no. of trips of the larger truck
then
(x+18) = no. of trips the smaller truck
:
Small truck tonnage - large truck tonnage = 12 tons
3(x+18) - 4x = 12
3x + 54 - 4x = 12
3x - 4x = 12 - 54
-x = -42
x = 42 trips by the large truck
then
42 + 18 = 60 trips by the small truck
;
:
Check solution
3(60) - 4(42) =
180 - 168 = 12
Question 240735: If I travel to point A going 50 kilometers an hour and it takes ten minutes how long will it take to reach point A going 40 kilometers an hour
Answer by Stitch(43) (Show Source):
You can put this solution on YOUR website!First lets convert km/hour to km/min
Now we know that it took 10min going 50km/h.
So if we take the  and multiply it by 10 min, you will get the distance traveled.
Lets convert 40km/h to km/min
To find the time, divide the distance by the speed
It will take 12.5min
Question 240717: One car travels 20 km/hr faster than another. While one of them travels 240 km, the other travels 180 km. Find the speed of the fast car.
Answer by solver91311(5072)  (Show Source):
Question 240662: One car traveling 40 Km/hr left a certain place 4 hours later than another car traveling in the same direction at the rate of 30 km/hr. In how many hours will the faster car overtake the other?
Answer by checkley77(7068) (Show Source):
You can put this solution on YOUR website!D=RT
D=30T
D=40(T-4)
SEEING AS THE 2 DISTANCES ARE THE SAME THEN:
30T=40(T-4)
30T=40T-160
30T-40T=160
-10T=-160
T=-160/-10
T=16 HOURS THEY WILL MEET.
PROOF:
30*16=40(16-4)
480=40*12
480=480
Question 240589: Dr. Pepper left Oakville at 9:00AM and drove to Central City at 60 km/h H. Salt left Oakville at 11:00AM and traveled the same route to Central City. If both mean arrived in Central City at 4:00PM, at what rate did H. Salt travel?
Answer by stanbon(26284) (Show Source):
You can put this solution on YOUR website!Dr. Pepper left Oakville at 9:00AM and drove to Central City at 60 km/h H. Salt left Oakville at 11:00AM and traveled the same route to Central City. If both mean arrived in Central City at 4:00PM, at what rate did H. Salt travel?
---------------------------------
Pepper DATA:
rate = 60 km/h ; time = 7 hrs ; distance = rt = 420 km
------------------------------------------
Salt DATA:
time = 5 hrs;
distance = 420 km ;
----------------------------------
rate = distance/time = 420/5 = 84 km/h
==============================================
Cheers,
Stan H.
Question 240575: you want to jog three miles in 45 mins.What must your speed be in miles per hour?
Answer by College Student(210)  (Show Source):
You can put this solution on YOUR website!To convert minutes to hours, we can use a convertion factor of 60 minutes per 1 hour in order tocancel out the unit of measure (minutes).
So, our mathematical equation would read like this:
.
(3 miles / 45 minutes) x (60 minutes / 1 hour)
.
or...
.
.
Your response is 4 miles per hour.
.
**************
Another way of doing it is to divide 45 by 3, which gives us 1 mile per 15 minutes. Since we know 60 minutes is 1 hour and 1 hour has 4 times 15 minutes, we arrive to the same conclusion... 4 miles per hour.
**************
Question 240572: if d=rt,and if r=60 and t=4,what does d equal?
Answer by rfer(2688) (Show Source):
Question 240511: I need to solve the following word problem using the system of linear equations in two variables. The word problem I am having trouble with is:
Traveling with the current, a canoe can go 48 miles in 4 hours. traveling against the current, it takes 6 hours to go the same distance. find the speed of the canoe in still water.
I came up with the following linear equations:
12=x+y for speed of canoe with current
8=x-y for speed of canoe against current
I solved for each variable and came up with x=10, y=2.
My question is which one is the correct answer for finding the speed of the canoe in still water? My thought is it is x=10.
Please help
Answer by checkley77(7068) (Show Source):
You can put this solution on YOUR website!D=RT OR R=D/T
R=48/4=12 MPH WITH THE CURRENT.
R=48/6=8 MPH AGAINST THE CURRENT
(12-8)/2=4/2=2 MPH IS THE RATE OF THE CURRENT.
PROOF:
12-2=10 MPH SPEED OF THE CANOE IN STILL WATER.
8+2=10 DITTO.
Question 240512: I need to solve the following word problem using the system of linear equations in two variables. The word problem I am having trouble with is:
Traveling with the current, a canoe can go 48 miles in 4 hours. traveling against the current, it takes 6 hours to go the same distance. find the speed of the canoe in still water.
I came up with the following linear equations:
12=x+y for speed of canoe with current
8=x-y for speed of canoe against current
I solved for each variable and came up with x=10, y=2.
My question is which one is the correct answer for finding the speed of the canoe in still water? My thought is it is x=10.
Please help
Answer by checkley77(7068) (Show Source):
You can put this solution on YOUR website!D=RT OR R=D/T
R=48/4=12 MPH WITH THE CURRENT.
R=48/6=8 MPH AGAINST THE CURRENT
(12-8)/2=4/2=2 MPH IS THE RATE OF THE CURRENT.
PROOF:
12-2=10 MPH SPEED OF THE CANOE IN STILL WATER.
8+2=10 DITTO.
Question 240428: SOLVE:
ERIN RIDES HER BIKE AT A CONSTANT SPEED FOR 21 MILES. SHE THEN RETURNS HOME AT THE SAME SPEED BUT TAKES A DIFFERENT ROUTE. HER RETURN TRIP TAKES ONE HOUR LONGER AND IS 26 MILES. FIND HER SPEED.
Answer by stanbon(26284) (Show Source):
You can put this solution on YOUR website!SOLVE:
ERIN RIDES HER BIKE AT A CONSTANT SPEED FOR 21 MILES. SHE THEN RETURNS HOME AT THE SAME SPEED BUT TAKES A DIFFERENT ROUTE. HER RETURN TRIP TAKES ONE HOUR LONGER AND IS 26 MILES. FIND HER SPEED.
---
1st Leg:
distance = 21 miles ; rate = x mph ; time = 21/x
--------------------
2nd Leg:
distance = 26 miles ; rate = x mph ; time = 26/x
------------------------------
Equation:
2nd time - 1st time = 1 hr
26/x - 21/x = 1
26 - 21 = x
x = 5 mph
-------------------
Cheers,
Stan H.
Question 240302: What formula is utilized to answer: if vehicle A and vehicle B leave from the same location, traveling same direction but at different speeds how many miles will it take vehicle B to Catch vehicle A if B is going 120 mph and A is going 100 MPH?
Answer by stanbon(26284) (Show Source):
You can put this solution on YOUR website!What formula is utilized to answer: if vehicle A and vehicle B leave from the same location, traveling same direction but at different speeds how many miles will it take vehicle B to Catch vehicle A if B is going 120 mph and A is going 100 MPH?
-----------------------
distance = rate*time
-----------------------
B DATA:
rate = 120 mph ; distance = x miles; time = x/120 hrs
----------------------------
A DATA:
rate = 100 mph ; distance = x miles ; time = x/100 hrs
-----------------------
Note: To have a problem the two vehicles have to leave the
starting point at different times.
Ex: Say that car A leaves 1 hr before car B; you get the following equation:
time A - time B = 1 hr
x/100 - x/120 = 1
120x - 100x = 100*120
20x = 100*120
x = 600 miles
B will catch A at the 600 mile marker.
===========================================
Cheers,
Stan H.
Question 240270: a train traveled m miles from the station. if it travels 87 miles more how far will it be from the station
Answer by stanbon(26284) (Show Source):
You can put this solution on YOUR website!a train traveled m miles from the station. if it travels 87 miles more how far will it be from the station
---
m+87 miles
==================
Cheers,
Stan H.
Question 240198: Train A and Train B are traveling in the same direction. Train A is traveling 120 mph, Train B is traveling 150 mph. If train A leaves the station at 2:30am, and Train B leaves the same station at 5:30am, what time will Train B catch up to Train A?
Answer by stanbon(26284) (Show Source):
You can put this solution on YOUR website!Train A and Train B are traveling in the same direction. Train A is traveling 120 mph, Train B is traveling 150 mph. If train A leaves the station at 2:30am, and Train B leaves the same station at 5:30am, what time will Train B catch up to Train A?
---------------------------------------------------
Train A DATA:
rate = 120 mph ; distance = x miles ; time = d/r = x/120 hrs.
-------------------------
Train B DATA:
rate = 150 mph ; distance = x miles ; time = x/150 hrs
-------------------------------------------
Equation:
time A - time B = 3 hrs.
x/120 - x/150 = 3
(150x - 120x) = 3*120*150
30x = 360*150
x = 360*5
x = 1800
----------------
Time for B to catch A: 1800/150 = 12 hrs.
Clock time will be 5:30 PM
===================================
Cheers,
Stan H.
Question 240099: Two cars depart form the same place. One heads north at a certain speed, and the other car heads east at a speed 7mph faster than the first car. After one hour the cars are 17 miles apart. How fast is each car traveling?
Answer by solver91311(5072) (Show Source):
Question 239947: At 8:00 am the smiths left a campground driving at 48 mi/hour. At 8:20 the Garcias left the same campground and followed the same route driving at 60 mi/hour. At what time did they overtake the Smiths?
I thought that I had to take 20/60 to get 1/3, to make minutes into hours, and add it to 60t. Then have 48t equal that. (Shown Below)
48t = 60(t+1/3)
Then, I distributed, and got:
48t = 60t + 20
I subtracted 60t from 48t, and got this:
-28t = 20
I divided 28 by 20, and got 1.4, but I'm not sure if my answer is right. Can you help me?
Answer by scott8148(3382)  (Show Source):
You can put this solution on YOUR website!you've got the times and speeds reversed
they overtake when they have travelled the same DISTANCE (rate x time)
the shorter time goes with the faster speed
60 t = 48 (t + 1/3) ___ the Smiths had a 20 min head start
12 t = 16 ___ t = 4/3 or 1:20
8:20 + 1:20 = 9:40
Question 239890: How far would one travel @ 20 mph for 35 seconds?
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!Distance = Velocity * Time
.
D = 20 mi / hr * 35 sec * 1 hr / 3600 sec
.
D= .1944 mile * 5280 ft / 1 mi
.
D= 1026.67 ft
.
.
.
check,,,v = (1026.67 ft * 1 mi/5280 ft) /(35 sec* 1hr/3600sec)= 20 mi / hr,,,,ok
Question 239900: Let?s say that you are driving on a straight route to a set
destination, and you can drive at any speed you like. You
stop for a few minutes but when you arrive at the halfway
point, you discover that you have averaged only 20 miles
per hour. So you decide to forego any more stops and drive
fast enough to average 40 miles per hour for the entire trip. If you keep a steady speed, how fast should you drive?
Answer by solver91311(5072) (Show Source):
Question 239884: I can not find the correct formula for the following problem:
Tina runs 10 miles in 70 minutes. How long does it take her to run 7 miles?
I have tried the Distance= rate x time but it doesn't make sense.
Found 2 solutions by solver91311, ankor@dixie-net.com:
Answer by solver91311(5072) (Show Source):
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!Tina runs 10 miles in 70 minutes. How long does it take her to run 7 miles?
:
Find her speed (mi/min): Speed = 
s = 10/70
s =  mi/min
:
Find the time:
Time =
t = 
invert the dividing fraction and multiply
t = 7 * 
t = 49 minutes to run 7 miles
Question 239818: if your driving 20 mph and it takes you 35 seconds to get from point a to point b how far of a distance is that
Answer by checkley77(7068) (Show Source):
Question 239829: the problem is" at 3:00p, two cars are 345 miles apart and are tavelling toward each other. if one car is travelling at 55mph and the other at 60mph, at what time will they meet?
Answer by checkley77(7068) (Show Source):
Question 239813: traveling at 20 mph how far will i travel in 35 seconds?
Answer by College Student(210) (Show Source):
Question 239731: one day a store sold 30 sweatshirts. white ones cost $9.95, and yellow ones cost $10.50. in all, $310.60 worth of sweatshirts were sold. how many of each color were sold?
Answer by unlockmath(117) (Show Source):
You can put this solution on YOUR website!Hello,
With this problem we can make two different equations. One equation can look like this where x will be the white sweatshirts and y will be the yellow sweatshirts.
x + y = 30 The other equation will look like this:
9.95(x)+ 10.50(y) = 310.60 We can solve this by substitution. Make the first equation like this:
x=30-y Then we plug this into the second equation.
9.95(30-y)+10.50(y)= 310.60 Notice we have just y so we can solve this:
298.50-9.95y+10.50y = 310.60 Combine like terms.
298.50+.55y=310.60 Subtract 298.50 from both sides.
.55y=12.10 Divide each side by .55
y=22 We're almost there. So we know there are 22 yellow sweatshirts. Plug this into the first equation and we'll find that there are 8 white sweatshirts.
Now to check to see if these are correct you can plug these answers into both equations and they should work out.
RJ Toftness
www.math-unlock.com
Question 239648: how longs it take to travel 240km at 100km/hr
Answer by Edwin McCravy(2922) (Show Source):
Question 239415: A biker completed a trip from town A to town B. If he rode 3 km per hour faster, then he could spend one hour less for this trip. If he rode 2 km per hour slower, he would be one hour late.
Find the distance between towns, speed of the biker, and time of traveling.
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!A biker completed a trip from town A to town B.
If he rode 3 km per hour faster, then he could spend one hour less for this trip.
If he rode 2 km per hour slower, he would be one hour late.
Find the distance between towns, speed of the biker, and time of traveling.
:
Let s = the biker's speed
then
(s+3) = 3 km faster speed
and
(s-2) = 2 km slower speed
:
Let d = dist from a to b
:
Write two time equations: time = dist/speed
 -  = 1 (he went 3 km/h faster)
and
 - = 1 (he went 2 km/hr slower)
:
Both equations = 1, so we can write it:
- = -
simplify, divide each term by d
 -  =  -
combine like terms
+ - =
:
 - =
:
Multiply by s(s+3)(s-2) to get rid of the denominators:
2(s+3)(s-2) - s(s-2) = s(s+3)
:
2(s^2 + s - 6) - s^2 + 2s = s^2 + 3s
:
2s^2 + 2s - 12 - s^2 + 2s = s^2 + 3s
Combine like terms on the left
2s^2 - s^2 - s^2 + 2s + 2s - 3s - 12 = 0
:
s - 12 = 0
s = 12 km/hr is the speed
:
Find the dist between towns using
- = 1
:
 -  = 1
Multiply by 60
5d - 4d = 60
d = 60 km is the distance
:
Find the time:  = 5 hrs, time of travel
:
:
Check solutions in:
- = 1
:
 - =
6 - 5 = 1 hr
Question 239249: Norfolk to Chadron
On Monday Chuck drove from Norfolk to Valentine averaging 47 mph.
On Tuesday he continued to Chadron averaging 69 mph.
His driving time on Monday was 2 hours longer than his driving time on Tuesday.
If the total distance from Norfolk to Chadron is 326 miles, than how many hours did he drive on Monday?
How far is Valentine to Chadron?
Answer by Photonjohn(42) (Show Source):
You can put this solution on YOUR website!The equation is
N to V is t=2
V to C is t
Distance is time x speed
N to V is 47 mph
V to C is 69 mph
47(t+2) + 69 t = 326
t = 2
Then N to V is 4 hours or 188 miles
and V to C is 2 hours or 138 miles
Question 239236: Against a head wind, Jeff computes his flight time for a trip of 2900 miles at 5 hours. The flight would take 4 hours and 50 minutes if the head wind were half as much. Find the head wind and the plane's air speed.
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!Against a head wind, Jeff computes his flight time for a trip of 2900 miles at 5 hours.
The flight would take 4 hours and 50 minutes if the head wind were half as much.
Find the head wind and the plane's air speed.
:
Let x = plane's air speed
Let y = headwind speed
and
.5y = half the headwind speed
:
Write two dist equations; dist = time * speed
:
Equation 1
5(x - y) = 2900
Simplify, divide both sides by 5
x - y = 580
and
equation 2
4  (x - .5y) = 2900
which is
 (x - .5y) = 2900
Divide both sides by 29/6: results
x - .5y = 600
:
use elimination
x - .5y = 600
x - y = 580
--------------Subtraction eliminate x, find y
+.5y = 20
y = 40 mph is the head wind
then
x - 40 = 580
x = 580 + 40
x = 620 mph is the plane speed
:
:
Check solution in the 2nd original equation
(620 - .5(40)) =
(620 - 20) =
(600) = 2900
29(100) = 2900
Question 239059: Suppose That A Flare Is Launched Upward With An Initial Velocity Of 80 Ft/sec From A Height Of 224 Ft. Its Height In Feet, H(t), After T Seconds Is Given By H(t) = -16t2 + 80t + 224 After How Long Will The Flare Reach The Ground?
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!Suppose That A Flare Is Launched Upward With An Initial Velocity Of 80 Ft/sec From A Height Of 224 Ft. Its Height In Feet, H(t), After T Seconds Is Given By H(t) = -16t2 + 80t + 224 After How Long Will The Flare Reach The Ground?
:
When the flare reaches the ground, H = 0, find t:
:
-16t^2 + 80t + 224 = 0
we can greatly simplify this, divide by -16
t^2 - 5t - 14 = 0
This factors to
(t-7)(t+2) = 0
Positive solution
t = 7 seconds after it is launched
;
;
Check this; replace x with 7 in the original equation
H = -16(7^2) + 80(7) + 224
H = -16(49) + 560 + 224
H = -784 + 784
H = 0
Question 239156: Two trains are traveling on parallel tracks.
Train A is going 40 mph and Train B is going 48 mph.
Train A will pass the station at 5:20 p.m.
Train B will pass the same station at 5:35 p.m.
At what time will Train B catch up to Train A?
Answer by Alan3354(6089) (Show Source):
You can put this solution on YOUR website! Two trains are traveling on parallel tracks.
Train A is going 40 mph and Train B is going 48 mph.
Train A will pass the station at 5:20 p.m.
Train B will pass the same station at 5:35 p.m.
At what time will Train B catch up to Train A?
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In the 15 mins from 520 to 535, train A goes 12 miles (48 x 1/4 hour)
Train B gains on train A at 8 mph (48-40)
12 miles/8 mph = 1.5 hours
535 + 130 = 7:05 PM
Question 239094: How many hours does it take if you are going 70 mph and have 395 miles left
Answer by checkley77(7068) (Show Source):
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