Questions on Word Problems: Travel and Distance answered by real tutors!

Tutors Answer Your Questions about Travel Word Problems (FREE)

Question 752120: If you are traveling @ 80 M.P.H how long will it take you to go 80 Miles?
I said 1 hour but I was told I was wrong? Can you help me?
Answer by josmiceli(9686)

(Show Source):

You can put this solution on YOUR website!
80 mi/hr says you travel 80 miles in 1 hour
You are right
(1) Did the problem get copied wrong somehow?
(2) The given answer could be wrong
???

Question 752097: 9. If a driver averages 50 miles per hour, the number of hours it will take to drive 360 miles is
Answer by rfer(12662)

(Show Source):

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360/50=7.2 hrs=7 hrs 12 min

Question 752026: Bert is traveling 15 miles per hour slower than Ernie. Bert can travel 150 miles in the same time it takes Ernie to go 225 miles. Find Bert's speed.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(57361)   (Show Source):
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Bert is traveling 15 miles per hour slower than Ernie. Bert can travel 150 miles in the same time it takes Ernie to go 225 miles. Find Bert's speed.
-----
Ernie DATA:
distance = 225 miles ; rate = x mph ; time = d/r = 225/x hrs.
-------
Bert DATA:
distance = 150 miles ; rate = x-15 mph ; time = d/r = 150/(x-15) hrs
----------
Equation:
time = time
225/x = 150/(x-15)
---
225x - 225*15 = 150x
75x = 225*15
x = (1/5)(225)
x = 45 mph (Ernie's rate)
x -15 = 30 mph (Bert's rate)
================================
Cheers,
Stan H.
==================

Answer by josmiceli(9686)   (Show Source):
You can put this solution on YOUR website!
Let = Ernie's speed
= Bert's speed
Let = time in hours for both
-----------------------------
Ernie's equation:
(1)
Bert's speed:
(2)
---------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
and
(1)
(1)
and

Bert's speed is 30 mi/hr
check:
(2)
(2)
(2)
OK

Question 751989: A car driving down a two lane highway has a speed of 50mph for the first part of the trip and 60 mph for the second part of the trip. The total time for the trip is 11 hrs and the total distance is 630 miles. Write a system of equations modeling the trip.
Answer by richwmiller(9143)   (Show Source):
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x+y=630,
X+Y=11,
50*X=x,
60*Y=y
x = 150, X = 3, y = 480, Y = 8
50*3=150
60*8=480

Question 751913: if you run 12ft per hour and your friend runs 10ft per hour but gets a 1000 feet head start how long will it take you to catch up

Answer by josmiceli(9686)   (Show Source):
You can put this solution on YOUR website!
Start a stop watch when you start running
Let = time in hrs for you to catch friend
Let = distance in ft you travel to catch friend
-------------------
Your equation:
(1)
Friend's equation:
(2)
--------------------
Substitute (1) into (2)
(2)
(2)
(2) hrs
You will catch up in 500 hrs
check:
(1)
(1) ft
and
(2)
(2) ft
OK
Note that = 20 days and 20 hrs

Question 526926: what is the speed if a car traveled 400km in 5hr
Answer by josh's girl(6)   (Show Source):
You can put this solution on YOUR website!
80km

Question 751437: 5 hens lay 6 eggs every 2 days.How many eggs will 25 chickens lay in 40 days?

Answer by ankor@dixie-net.com(15656)   (Show Source):
You can put this solution on YOUR website!
5 hens lay 6 eggs every 2 days.
Find the number of hen-days per egg
= hen-days per egg
:
How many eggs will 25 chickens lay in 40 days?
Invert the dividing fraction and multiply
(25*40) * = 600 eggs

Question 751586: A boat travels 6 miles in 2 hours upstream and 5 miles in 1 hour downstream. Find the speed of the boat and the speed of the current if both speeds are constant.
Answer by stanbon(57361)   (Show Source):
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A boat travels 6 miles in 2 hours upstream and 5 miles in 1 hour downstream. Find the speed of the boat and the speed of the current if both speeds are constant.
Upstream DATA:
distance = 6 miles ; time = 2 hrs ; rate = 6/2 = 3 mph
----
Downstream DATA:
distance = 5 miles ; time = 1 hr ; rate = 5/1 = 5 mph
------
Equations:
b + c = 5 mph
b - c = 3 mph
----
2b = 8
boat in still water = 4 mph
-----
Solve for "c":
b + c = 5
4 + c = 5
c = 1 mph (speed of the current)
================
Cheers,
Stan H.
================

Question 751490: Travelling@ 29mph what distance covered in 1.4 seconds

Answer by stanbon(57361)   (Show Source):
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Travelling@ 29mph what distance covered in 1.4 seconds
distance = rate*time
distance = (29 miles/hr)[(1.4/3600)hr] = 0.0113 miles
------------
cheers,
Stan H.

Question 750996: The distance from Dayton to Indianapolis is 120 miles and it is 180 miles from Indianapolis to Chicago. If a car needs 4 gallons of gasoline to drive from Dayton to Indianapolis, how many gallons of gasoline will it need to drive to Chicago from Dayton?
Answer by Cromlix(353)   (Show Source):
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If the car requires 4 gallons of gas to drive 120 miles
This equates to 1 gallon every 30 miles.
The distance from Dayton to Chicago is 300 miles
Therefore the car will require 10 gallons of gas.
300/30 = 10.
Hope this helps
:-)

Question 751430: A girl walks 5 miles in 2 hours. what is her average speed in meters per second?
Answer by Cromlix(353)   (Show Source):
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5 miles = 8046.72 metres
2 hours = 7200 seconds
Divide 8046.72 by 7200
= 1.11 metres/sec.

Question 751433: an arrow is shot into the air from a building that is 32ft high. the height of the arrow after t seconds is given by the formula h(t)=-16t^2+48t+32=0
when will the arrow hit the ground?

Answer by jim_thompson5910(28595)   (Show Source):
You can put this solution on YOUR website!
Solve for t

Use the quadratic formula to solve for t

Plug in , ,

or

or

or

or

Ignore the negative solution (since a negative time doesn't make sense)

So the only solution is approximately

This means it will take approximately 3.561553 seconds for it to hit the ground.

Question 751409: A girl walks 5 miles in 2 hours. What is her average speed in miles per hour?

Answer by jim_thompson5910(28595)   (Show Source):
You can put this solution on YOUR website!
Speed = Distance/Time

Speed = 5 miles/2 hours

Speed = 2.5 miles/1 hour

Speed = 2.5 miles per hour

Question 751227: suppose you ride your bike 350 meters in 10 seconds. what is your average speed?
Found 2 solutions by Edwin McCravy, jim_thompson5910:
Answer by Edwin McCravy(8909)   (Show Source):
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350 meters in 10 seconds means 350 meters per 10 seconds which means 350 meters divided by 10 seconds which means 350 meters OVER 10 seconds which means and we abbreviate meters as m and seconds as s which means which means which mens 35 meters per second. Edwin

Answer by jim_thompson5910(28595)   (Show Source):
You can put this solution on YOUR website!
350 m/10 sec = 35 m/s is your average speed

Question 751115: A race car driver averaged 140 miles/hour. If the driver completed the race in 2 and a half hours how long was the race?
Answer by josmiceli(9686)   (Show Source):
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The race was 150 miles long

Question 751119: Two cars are traveling on the same road and start from the same location. When the blue car starts the trip the red car has already traveled 40 miles. The speed of the blue car is 70 mph and the speed of the red car is 50 mph
a). How long does it take the blue car to catch the red car?
b). How far have they traveled from the starting point when the blue car catches the red car?

Answer by josmiceli(9686)   (Show Source):
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Let = the time in hours it takes blue car to catch red car
Let = the distance in miles blue car has to travel to catch red car
-----------------
Blue car's equation:
(1)
Red car's equation:
(2)
------------------
Substitute (1) into (2)
(2)
(2)
(2)
-------------
(1)
(1)
(1)
---------------
a). It takes 2 hours for the blue car to catch the red car
b). They traveled 140 miles from the starting point when the blue car catches the red car
---------------
check answer:
(2)
(2)
(2)
OK

Question 750916: Two cruise ships set sail from Florida on the same day. One makes a round trip every 12 days. The other makes a round trip every 16 days. In how many days will both cruise ships be in Florida?
Answer by JoeTaxpayer(135)   (Show Source):
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You seek the least common multiple of 12 and 16.
12 is 2*2*3
16 is 2*2*2*2
These are the prime factors for each. Combined, we need (2^4)*3 or 48 days they will both be back at Fla port.

Question 750824: If a woman jogs at a speed of 4 mph over a distance of 2 miles. How much time did it take her for the run?
Answer by stanbon(57361)   (Show Source):
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If a woman jogs at a speed of 4 mph over a distance of 2 miles. How much time did it take her for the run?
------
time = distance/rate
time = 2 miles/4 mph = (1/2) hr
====================
Cheers,
Stan H.
====================

Question 750787: kelly rides her bike from city A to city B , how long is her ride
Answer by tommyt3rd(591)   (Show Source):
You can put this solution on YOUR website!
please repost your question it seems to be missing information :)

Question 750630: A pilot can fly a plane at 125 mph in calm air. A recent trip of 300 mi flying with the wind and 300 mi returning against the wind took 5 h. Find the rate of the wind
Answer by lwsshak3(6513)   (Show Source):
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A pilot can fly a plane at 125 mph in calm air. A recent trip of 300 mi flying with the wind and 300 mi returning against the wind took 5 h. Find the rate of the wind.
***
let x=rate of speed of wind
125+x=rate of speed with wind
125-x=rate of speed against wind
travel time=distance/rate of speed
..
300/(125+x)+300/(125-x)=5
divide by 5
60/(125+x)+60/(125-x)=1
LCD:(125+x)(125-x)
60(125-x)+60(125+x)=(125^2-x^2)
7500-60x+7500+60x=15625-x^2
15000=15625-x^2
x^2=625
x=25
rate of speed of wind=25 mph

Question 750583: two cars leave from a city at the same time and travel in the same direction.One car travels one-third and two-third times as fast as the other. After 3 hr. they are 150 mi apart. What are the speeds of the cars?

Answer by josgarithmetic(1530)   (Show Source):
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What are you saying here, in the description, "One car travels one-third and two-third times as fast as the other."? That is meaningless.

I'll try to guess what you mean.

________________rate________________time________________distance
Fast Car____________________(3)_______________
Slow Car________u__________________(3)________________

The distance reached for the fast car is greater than the distance reached for the slow car. Their difference is 150 miles. I AM GUESSING AS WELL AS I CAN THAT YOU WANTED TO SAY "one and two thirds times the other", for how to relate the speeds or the cars.

We may want to solve for u in .

You could describe again more carefully the problem description in case I did not guess what you really meant.

Question 750288: A student must leave for campus in 10 minutes or he will be late for class. Unfortunately, he is snowed in. He can shovel the driveway in 16 minutes, and his brother claims to be able to do it in 14 minutes. If they shovel together, how long will it take to clear the driveway? Will this give enough time for the student to get to the campus?
It will take about ____ minutes to clear the driveway together.
Will this give the student enough time to get to the campus?
I tried to solve this and came up with the wrong answer and am hoping I can find out where I am wrong. It will take about __x__ minutes to clear the driveway together. So, 1/x =1/14+1/16 x = 7.47
So It will take about __7.47__ minutes to clear the driveway together. I also tried 8 and it was also wrong, thank you!
This will give the student enough time to get to the campus
Answer by ankor@dixie-net.com(15656)   (Show Source):
You can put this solution on YOUR website!
A student must leave for campus in 10 minutes or he will be late for class.
Unfortunately, he is snowed in.
He can shovel the driveway in 16 minutes, and his brother claims to be able to do it in 14 minutes.
If they shovel together, how long will it take to clear the driveway?
Will this give enough time for the student to get to the campus?
:
Use a shared work equation, let t = time working together
Let the completed job = 1 (a cleared driveway)
:
+ = 1
multiply equation by the least common multiple of 16 and 14, that 112, results:
7t + 8t = 112
15t = 112
t = 112/15
t = 7.47 minutes, so you are right!

Question 750516: what are the zeros of the quadratic equations
22=6x^2+13
y=2x^2-11x
y=x^2+x-12
Please show work, thank you.
Answer by lwsshak3(6513)   (Show Source):
You can put this solution on YOUR website!
what are the zeros of the quadratic equations
22=6x^2+13
6x^2=9
x^2=9/6=3/2
x=±√(3/2)
..
y=2x^2-11x
2x^2-11x=0
x(2x-11)=0
x=0
or
x=11/2
..
y=x^2+x-12
x^2+x-12=0
(x+4)(x-3)=0
x=-4
or
x=3

Question 750544: A boat takes 8 hours to go 6 miles upstream and come back to the starting point. If the speed of the boat is 4 miles per hour in still water, what is the rate of the current?
Answer by stanbon(57361)   (Show Source):
You can put this solution on YOUR website!
A boat takes 8 hours to go 6 miles upstream and come back to the starting point. If the speed of the boat is 4 miles per hour in still water, what is the rate of the current?
-------
Upstream DATA:
time = x hrs ; distance = 6 miles ; rate = d/t = 6/x hrs
----
Downstream DATA:
time = 8-x hrs ; distance = 6 miles ; rate = d/t = 6/(8-x)
--------
Equation:
Upstream Rate Eq::: 4-c = 6/x
Downstream Rt Eq::: 4+c = 6/(8-x)
----------------
Add to solve for "x":
8 = (6/x)+(6/(8-x))
-----
8x(8-x) = 6(8-x) + 6x
-----
64x - 8x^2 = 48
---
x^2 - 8x + 48 = 0
-----
No Real Number solution.
================
Cheers,
Stan H.
================

Question 750379: Aya rode her bicycle from her house to a friend's house, averaging 16 kilometers per hour. It turned dark before she ready to return home, so her friend drove her home at a rate of 80 kilometers per hour. If Aya's total traveling time was 3 hours, how far away did her friend live?
Answer by ankor@dixie-net.com(15656)   (Show Source):
You can put this solution on YOUR website!
Aya rode her bicycle from her house to a friend's house, averaging 16 kilometers per hour.
It turned dark before she ready to return home, so her friend drove her home at a rate of 80 kilometers per hour.
If Aya's total traveling time was 3 hours, how far away did her friend live?
:
let d = one way distance to friend's house
:
Write a time equation: time = dist/speed
:
bike time + ride time = 3 hrs
+ = 3
multiply by 80 to clear the denominators
5d + d = 80(3)
6d = 240
d = 240/6
d = 40 mi to fr house
:
:
Confirm this by finding the total of the time each way
40/16 = 2.5 hrs
40/80 = .5 hrs
----------------
total: 3 hrs

Question 750452: A car movin at 60 km/h covers a journey in 4 hours.how long will it take to cover the journey if its speed is reduced to 45km/h
Answer by checkley79(3050)   (Show Source):
You can put this solution on YOUR website!
45/60=4/x
60*4=45x
240=45x
x=240/45
x=5 hours & 20 minutes.

Question 750453: How long is the distance of bird key park and Sarasota's Bay Front Park?
Answer by Alan3354(30993)   (Show Source):
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How long is the distance of bird key park and Sarasota's Bay Front Park?
--------------
That's not something that can be calculated.
Look it up somewhere.
---------------
PS "How long is the distance..." is gibberish

Question 750279: A truck can travel 140 miles in the same time it takes a car to travel 180 miles. If the trucks rate is 10 miles per hour slower than the cars, find the average rate for each.
The rate of the car is ____ miles per hour.
The rate of the truck is ____ miles per hour.
Answer by ankor@dixie-net.com(15656)   (Show Source):
You can put this solution on YOUR website!
A truck can travel 140 miles in the same time it takes a car to travel 180 miles.
If the trucks rate is 10 miles per hour slower than the cars, find the average rate for each.
:
let s = the speed of the truck
then
(s+10) = speed of the car
:
Write a time equation: time = dist/speed
+
Cross multiply
180s = 140(s+10)
180s = 140s + 1400
180s - 140s = 1400
40s = 1400
s = 1400/40
s = 35 mph is the speed of the truck
:
I'll let you find the speed of the car. Check your solutions by finding the
actual time of each, they should be equal

Question 750363: How long takes a car traveling at 35 mph travel 1000 feet?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(9686)   (Show Source):
You can put this solution on YOUR website!
You can convert ft to miles
In terms of units:
( feet ) x ( miles / feet ) = miles

----------------

hrs
Convert hours to seconds
( hours ) x ( min ) / hour ) x ( sec / minute )

It takes 19.5 seconds to go 1000 ft

Answer by Alan3354(30993)   (Show Source):
You can put this solution on YOUR website!
How long takes a car traveling at 35 mph travel 1000 feet?
--------------
15 mi/hr = 22 ft/sec (trust me or work it out)
---
35 mi/hr = 35*22/15 ft/sec = 154/3 ft/sec
-----
d = r*t
t = d/r = 1000/(154/3)
t = 3000/154 sec
t =~ 19.48 seconds

Question 750340: a motorcycle is travelling at 55 kilometers per hour how far will it go in four hours
Answer by obulee(5)   (Show Source):
You can put this solution on YOUR website!
if d traveller travels 55km per hr, den in four hrs d traveller will travel 55 multiply by four=220km

Question 750326: 25 miles average speed of 50 mph how long would it take?
Also
25 miles average speed of 60 mph how long would it take?
Answer by dkppathak(43)   (Show Source):
You can put this solution on YOUR website!
speed=distance / time
time =distance / speed
time taken =25/50houres
= 1/2 hours = 30 minutes
similarly
we can solve the other
time =25/60 =5/12 h
=5/12 multiplied by 60
= 25 minutes
answer 30 minutes
25 minutes

Question 750301: Please help me solve this word problem:
Jerry takes 6 hours to ride a bicycle 30 minutes against the wind. He takes two hours to return with the wind. Find Jerry's average riding speed in still air and the average speed of the wind.
*thank you ^_^*
Answer by lwsshak3(6513)   (Show Source):
You can put this solution on YOUR website!
Jerry takes 6 hours to ride a bicycle 30 miles against the wind. He takes two hours to return with the wind. Find Jerry's average riding speed in still air and the average speed of the wind.
***
I assume you mean 30 miles instead of 30 minutes
let x= Jerry's average riding speed in still air
let c= Average speed of the wind
x+c=speed with the wind
x-c=speed against the wind
travel time=distance/speed
30/(x-c)=6
30/(x+c)=2
..
6x-6c=30
2x+2c=30
..
6x-6c=30
6x+6c=90
add
12x=120
x=10
2c=30-2x
2c=30-20=10
c=5
Jerry's average riding speed in still air=10 mph
Average speed of the wind=5 mph

Question 750289: A train is traveling east at 124 miles per hour. Which direction is it traveling?
Answer by tommyt3rd(591)   (Show Source):
You can put this solution on YOUR website!
East. Maybe this question needs more details. Re-post if needed

:)

Question 750284: The speed of a stream is 2 mph. A boat travels 8 miles upstream in the same time it takes to travel 12 miles downstream. What is the speed of the boat in still water?
The speed is ___ mph.
Answer by tommyt3rd(591)   (Show Source):
You can put this solution on YOUR website!
we solve as a proportion:

downstream
(v+2)t=12
t=12/(v+2)

upstream:
by same reasoning
t=8/(v-2)

setting t's equal and simplifying

v=10 mph

:)

Question 750272: Sam drove 200 miles at an average rate of speed of 50 miles per hour.How long did he travel which one is the answer t=200/50 t=200*50 or t=50/200
Answer by Cchristman(1)   (Show Source):
You can put this solution on YOUR website!
t=200/50= 4 hours.

Question 750254: A truck traveled the first 200 miles of a trip at one speed and the last 225 miles at the average speed of 5 mph less. the entire trip took 10 hours. what were the two average speeds?
So far I have tried 200x+250(x-5)=10 and I got x=2.8 and -2.2 which is obviously wrong. Please help!
Answer by josgarithmetic(1530)   (Show Source):
You can put this solution on YOUR website!
Basic concept is rate*time=distance. rate is miles per hour, time is hours, distance is miles.

You know the total time but you do not know each individual time for the two distances. Know to do this:

---------which you can use.

First Part, rate is r.
Second part, rate is r-5.

The sum of the two parts of the times for the trip is 10 hours. See, the equation has some rational parts, meaning take the form of fractions.

Question 750121: 1.3 person starts walking on circular track at speed of 10,20 & 40 mtr per sec.Where they will meet on 1km circular track?
3 person starts walking on 1km long track at speed of 10,20 & 40 mtr per sec.Where they will meet ?
Answer by stanbon(57361)   (Show Source):
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3 persons start walking on 1km long track at speed of 10,20 & 40 mtr per sec. Where they will meet ?
-------
At 10 m/sec the time for one oval is 1000/10 = 100 seconds
At 20 m/sec the time for one oval is 1000/20 = 50 seconds
At 40 m/sec the time for one oval is 1000/40 = 25 seconds
------
least common multiple is 100.
They will meet at the start/finish line:
The 10 m/sec will have gone 1 lap
The 20 m/sec will have gone 2 laps
The 40 m/sec will have done 4 laps
===========================================
Cheers,
Stan H.
============

Question 750139: Thor's average driving speed is 15 kilometers per hour faster than Doug's. in the same length of time it takes Thor to drive 267 kilometers, Doug drives only 222 kilometers.What is Thor's average speed?
Answer by stanbon(57361)   (Show Source):
You can put this solution on YOUR website!
answered

Question 750141: Thor's average driving speed is 15 kilometers per hour faster than Doug's. in the same length of time it takes Thor to drive 267 kilometers, Doug drives only 222 kilometers.What is Thor's average speed?
Answer by stanbon(57361)   (Show Source):
You can put this solution on YOUR website!
Thor's average driving speed is 15 kilometers per hour faster than Doug's. in the same length of time it takes Thor to drive 267 kilometers, Doug drives only 222 kilometers.What is Thor's average speed?
-------
Doug DATA:
distance = 222 km ; speed = x km/hr ; time = d/r = 222/x hrs
------
Thor DATA:
distance 267 km ; speed = x+15 km/hr ; time = 267/(x+15) hrs
-----------------
Equation:
time = time
222/x = 267/(x+15)
267x = 222x + 3330
45x = 3320
x = 74 km/hr (Doug's speed)
x+15 = 89 km/hr (Thor's speed)
-----------------
Cheers,
Stan H.
=================

Question 750132: Train A leaves a station traveling at 80 kilometers per hour. Four hours later, train B leaves the same station traveling in the same direction at 90 kilometers per hour. How long does it take train B to catch up to trian A?
Answer by sachi(392)   (Show Source):
You can put this solution on YOUR website!
see the solution of 750133

Question 750133: Train A leaves a station traveling at 80 kilometers per hour. Four hours later, train B leaves the same station traveling in the same direction at 90 kilometers per hour. How long does it take train B to catch up to trian A?
Answer by sachi(392)   (Show Source):
You can put this solution on YOUR website!
let train B catches A after x hrs
in x hrs b travels 90x km
& in x+4 hrs A travels 80(x+4) as A left 4 hrs before
now both distances are same
so 90x=80(x+4)=80x+320
or 10x=320
or x=32 hrs

Question 750129: A motorboat can go 12 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 12 miles. Whats the speed of the boat in still water?
Answer by stanbon(57361)   (Show Source):
You can put this solution on YOUR website!
A motorboat can go 12 miles downstream on a river in 20 minutes.
It takes 30 minutes for this boat to go back upstream the same 12 miles.
Whats the speed of the boat in still water?
---------
Downstream DATA:
dist = 12 miles ; time = 1/3 hr ; rate = d/t = 36 mph
----------------------
Upstream DATA:
dist = 12 miles ; time = 1/2 hr ; rate = d/t = 24 mph
---------------------
Equation:
Downstream: b + c = 36 mph
Upsteam ::: b - c = 24 mph
------------------------------
Solve for "b":
2b = 60 mph
b = 30 mph (speed of the boat in quiet water)
------
Solve for "c":
2C = 12 mph
c = 6 mph (speed of the current)
==================================
Cheers,
Stan H.
==============