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

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Question 994775: Ryan left the science museum and drove south. Gabriella left 3 hours later driving 42 km/h faster in an effort to catch up to him. After 2 hours Gabriella finally caught up. Find Ryan's average speed.
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PERSON        speed        time        distance
Ryan           r           3+2=5        r*5
Garbiella     r+42         2            (r+42)*2


The distance column is the "catch-up" distance, and each expression is the same quantity; the expressions are equal.

Question 994774: A plane flies 435 miles in the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15 miles per hour, find the speed of the plane in still air
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This is a very common form of uniform travel rates exercise. The solution here will be generalized.

RT=D relates rate (or speed), time, and distance.

VARIABLES

Direction           speed            time         distance
WITHWIND            r+w               t            D
AGAINSTWIND         r-w               t            d


Find the two expressions, formulas, for t.
Direction           speed            time         distance
WITHWIND            r+w              D/(r+w)       D
AGAINSTWIND         r-w              d/(r-w)       d


Those two times were given as equal.

The only unknown variable in this equation is r, the rate of the vehicle in still air.

SOLUTION STEPS FOR THE ARITHMETIC

Question 994764: It takes Erica, traveling at
24 mph,
50 minutes longer to go a certain distance than it takes Ricky traveling at
54 mph. Find the distance traveled.

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It takes Erica, traveling at 24 mph, 50 minutes longer to go a certain distance han it takes Ricky traveling at 54 mph. Find the distance traveled.
----------
Erica DATA::
rate = 24 mph ; distance = x miles ; time = x/24 hrs
-------------------
Ricky DATA:
rate = 54 mph ; distance = x miles ; time = x/54 hrs
---------------------------
Equation:
Erica time - Ricky time = (5/6) hr.
----
x/24 - x/54 = 5/6
-----
Multiply thru by 6 to get:
x/4 - x/9 = 5
-----
9x - 4x = 5*4*9
----
5x = 5*4*9
x = 36 miles
----
Cheers,
Stan H.
---------

Question 994570: A student starting from his house walk at a speed of 2.5 km per hour and reaches his school 6 minute late. Next day at the same time he increases his speed by 1 km per hour and reaches 6 minute early. The distance between his school and house is?
Found 2 solutions by MathTherapy, lwsshak3:
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A student starting from his house walk at a speed of 2.5 km per hour and reaches his school 6 minute late. Next day at the same time he increases his speed by 1 km per hour and reaches 6 minute early. The distance between his school and house is?
Distance:  km



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A student starting from his house walk at a speed of 2.5 km per hour and reaches his school 6 minute late. Next day at the same time he increases his speed by 1 km per hour and reaches 6 minute early. The distance between his school and house is?
let x=distance between his school and house is?
x/2.5-x/3.5=12 min=1/6 hr
x/2.5-x/3.5=1/6
lcd: 2.5*3.5
3.5x-2.5x=8.75/6
x=1.4583 km
between his school and house is? 1.4583 km

Question 994643: Randy made a business trip of 190 miles. His mean speed for the first part of the trip was 52 mph and 56 mph for the second part. If the total trip took 3 1/2 hours, how long did he travel at each rate?
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Let t = the amount of time he traveled at 52 mph.
Then 3.5 - t is the time he spent traveling at 56 mph.
Setting the equation up, we get
52t + 56(3.5 - t) = 190
52t + 196 - 56t = 190
-4t = -6
t = 1.5 hours
3.5 - t = 2.0 hours

Question 994689: A bicyclist traveling at 35 miles per hour, rides a total of120 miles. How much time does it take.
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Since rate times time equals distance, or rt=d, we can find the time by dividing distance by the rate. Thus
t = d/r = 120/35 = 3 3/7 hours or about 3.43 hours.

Question 994675: jane travels 6 time faster than bill traveling in opposite direction they are 378 miles apart after 4.5 hours find their rates of travel
Found 2 solutions by Alan3354, stanbon:
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Is it 6 times faster?
Or 6 times as fast?

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jane travels 6 time faster than bill traveling in opposite direction they are 378 miles apart after 4.5 hours find their rates of travel
------
Bill DATA:
rate = x mph ; time = 4.5 hrs ; distance = 4.5x miles
----
Jane DATA:
rate = 6x mph ; time = 4.5 hrs ; distance = 4.5*6x = 27x miles
-----
Equation:
dist + dist = 378 miles
4.5x + 27x = 378
31.5x = 378
-----
x = 12 mph (Bill's rate)
6x = 72 mph (Jane's rate)
--------
Cheers,
Stan H.
---------

Question 994599: David and Alice are 50 miles apart. david begins to drive towards alice at 50 miles per hour, and at the same time Alice drives towards david at 35 miles an hour. after 12 minutes, approximately how many feet are they away from each other?
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David and Alice are 50 miles apart. david begins to drive towards alice at 50 miles per hour, and at the same time Alice drives towards david at 35 miles an hour. after 12 minutes, approximately how many feet are they away from each other?
12 min=12/60=1/5 hr
distance=travel time*speed
1/5*50=10 mi (distance david traveled)
1/5*35=7 mi (distance alice traveled)
50-10-7=33 mi
5280*33=174240 ft
how many feet are they away from each other? 174240 ft

Question 994471: Assuming equal rates, 240 miles in 8 hours implies 255 miles in how many hours?

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.
x=number of hours for 255 miles
.
8 hrs/240 mi=x/255 mi
240 mi(x)=2040 mi-hrs
x=8.5 hrs
.
ANSWER: At the same rate, it would
take 8.5 hours to travel 255 miles.

Question 994507: Students are traveling in two cars to a football game 145 miles away. One car travels at an average speed of 40 miles per hour. The second car starts a half hour later and travels at an average speed of 50 miles per hour. How long will it take the second car to catch up to the first car?
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CAR            speed       time        distance
Fast Later       50        t             d
Slow Early       40        t+1/2         d

Important to understand,


Question 994514: An airplane flies 410 miles with the wind and 310 against the wind in the same length of time. If the speed of the wind is 40, what is the speed of the airplane in still air?
A.). 293mph. B). 288mph. C). 124mph. D). 278mph

I have tried this:
X=d/t.
X=410 -40
X=370
X=310+40
X=350

Found 2 solutions by josgarithmetic, macston:
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Assign some variables.

Uniform Rates Travel Rule, RT=D to relate rate, time, distance;
also can be used as R=D/T.
Direction   speed        time       distance
WITH        r+w           t          m
AGAINST     r-w           t          n


See that the same number in the same variable t is used for both directions. The question asks for r, but not for t.
Direction   speed        time              distance
WITH        r+w           t=m/(r+w)          m
AGAINST     r-w           t=n/(r-w)          n


Equate the two formulas for time t:

This equation uses only one unknown variable, r, which is what the question asks to find. Solve the equation for r.

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.
t=time; d=distance; r=rate
t=d/r
.
With wind:
t=410mi/r+40
Against wind:
t=310mi/r-40
.
Since time in both directions is the same:
410mi/r+40=310mi/r-40
410(r-40)=310(r+40)
410r-16400=310r+12400
100r=28800
r=288
.
ANSWER: The rate of the plane in still air is 288 mph.

Question 994497: If I am riding a bike at 18 mph and my friend is riding 3 miles ahead at 12 mph. How long before I catch up to him?
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Let = distance in miles you travel
until you catch friend
Let = time in hours it takes you
to catch friend
-----------------------
Friend's equation:
(1)
(2)
-----------------
Substitute (2) into (1)
(1)
(1)
(1)
---------------
You will catch friend in 1/2 hr
---------------
check:
(2)
(2)
and
(1)
(1)
(1)
OK

How long would it take for a ball dropped from the top of a 289-foot building to hit the ground? Round your answer to two decimal places.

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.
t=time; d=distance; g=acceleration of gravity=32ft/s^2
.

.

.

.

.
ANSWER: It will take 4.25 seconds for the ball to hit the ground.

Question 994428: It took Mary 15 seconds to walk 10 feet.How fast was she walking,in feet per second?
Found 2 solutions by Alan3354, Cromlix:
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To find ft/sec, divide the feet by the seconds.

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Hi there,
It took Mary 15 seconds to walk 10 feet.
Speed = Distance/Time
Speed = 10 feet/ 15 seconds
Speed = 0.67 feet per second (2 decimal places)
Hope this helps :-)

Question 994436: If you run 15 miles in 120 minutes. At this speed how long will it take you to run 125 miles?
Found 2 solutions by Cromlix, stanbon:
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Hi there,
15 miles in 120 minutes
1 mile in 8 minutes.
125 miles in 8 x 125
125 miles in 1000 minutes
125 miles in 16 hrs 40 minutes.
Hope this helps :-)

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If you run 15 miles in 120 minutes. At this speed how long will it take you to run 125 miles?
-------
Note:: 120 min = 2 hrs
15 miles in 2 hrs = 7.5 mph
------
Equation:
time = distance/rate
time = 125/7.5 = 16 2/3 hrs
------------
Cheers,
Stan H.
---
Or use a proportion:
x/125 = 2/15
x = 250/15 = 16 2/3 hrs

Question 994421: It is 185 miles to Fort Worth. If Vang drives
2 hours at 65 miles per hour, how far will he be from Fort Worth?
5. Write and solve the arithmetic problem for each step.
Multiply the number of hours times the number of miles per hour.
Then subtract the number of miles driven from the total number of miles.
?
Write and solve the arithmetic problem for the first step.

7y8

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It is 185 miles to Fort Worth. If Vang drives
2 hours at 65 miles per hour, how far will he be from Fort Worth?
---
d = 185 - 2*65
----
d = 185 - 130
----
d = 55 miles
---------------
Cheers,
Stan H.
------------

Question 994424: I really need help deciphering this word problem:
Flying with the wind a plane went 299 mph. Flying into the same wind the plane only went 233 mph. What is the speed of the wind? How fast would the plane go if there were no wind?

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still air speed=x
wind speed =c
x+c=299
x-c=233
2x=532
x=266, dividing by 2 both sides.That is the speed of the plane in still air.

Question 994397: A woman can bicycle 92 miles in the same time as it takes her to walk 20 miles. She can ride 9 mph faster than she can walk. How fast can she walk?
Using r as your variable to represent the rate at which she walks, write an equation using the information as it is given above that can be used to solve this problem.
What's the equation needed to solve this problem?
How many mph does she walk?

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A woman can bicycle 92 miles in the same time as it takes her to walk 20 miles. She can ride 9 mph faster than she can walk. How fast can she walk?
Using r as your variable to represent the rate at which she walks, write an equation using the information as it is given above that can be used to solve this problem.
What's the equation needed to solve this problem?
How many mph does she walk?
------
Biking DATA:
dist = 92 miles ; rate = x+9 mph ; time = d/r = 92/(x+9) hrs
-----------------
Walking DATA:
dist = 20 miles ; rate = x mph ; time = d/r = 20/x hrs
---------------
Equations:
time = time
92/(x+9) = 20/x
-----
92x = 20(x+9)
92x = 20x + 180
72x = 180
x = 2.5 mph (walking)
x+9 = 11.5 mph (biking)
------------
Cheers,
Stan H.
----------

Question 994382: if i were to ride a bike to the moon; and i traveled non-stop until i got there, how many hours would it take me to get there if i traveled 15 miles an hour
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if i were to ride a bike to the moon; and i traveled non-stop until i got there, how many hours would it take me to get there if i traveled 15 miles an hour
-------------
You didn't spec the distance.
240,000 miles is close
---
d = r*t
t = d/r
240000/15 = 16000 hours

Question 994361: A motorcycle travels 47 miles in 3 hours. What is the biker's speed in feet per second?

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A motorcycle travels 47 miles in 3 hours. What is the biker's speed in feet per second?
-------------
47 mi/3 hr = 47*5280 ft/(3*3600 seconds)

Question 994168: Paddling 7 miles upstream, Sara and her brother averaged 2 miles per hour. On the way back, their rate of speed was 3.5 miles per hour. How long did it take them to make the round trip?
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               speed    time    distance
UPSTREAM         2       u       7
DOWNSTREAM       3.5     b       7
Total                   u+b


A bus traveled 3/5 of the distance between two cities in 1/4 hour. At this rate, how many hours will it take the bus to travel the entire distance between these two cities.

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Distance between cities may be d, but not need to be known.

t, how many hours to go distance d.
just using uniform travel rates rule.

Still t is a fraction of an hour.

, which is 25 minutes.

Question 994179: a car leaves New York traveling south at 50m/hr. One hour later another car leaves New York on the same road traveling south at 55m/hr. How far from New York will the faster car overtake the slower car?
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How far will the first car travel during that first hour? How long will it take the second car to travel that distance at the difference in their speeds?

John

My calculator said it, I believe it, that settles it

Question 994137: how far in kilometers, will a car travel in 3 hours at an avarage speed of 60km/h?

The total distance around the academic oval is 2.2 km. If a jogger can go around the oval 3 times in 1 hour, what is his speed in meters per second?
a.) 36 2/3
b.) 6 1/9
c.) 11/18
d.) 11/180
When I solve it, I multiply 2.2 km with three then convert it to meters (2.2 x 3 = 6.6km; 6.6km= 6600 m). After that, I convert 1 hour to seconds (60 mins x 60 seconds = 3600 seconds). After that, I divided 6600m with 3600seconds and get 11/6 as my answer. Ive asked my friends but they also get the same answer as mine. Help please!! Thank you!!!!

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You and your friends are correct.

Question 994091: amit walked 30 meters towards east,turned right and walked 40 meters and turned left and walked 30 meters.In which direction is he now from the starting point?
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amit walked 30 meters towards east,turned right and walked 40 meters and turned left and walked 30 meters.In which direction is he now from the starting point?
----
Start at (0,0)
30 east to (30,0)
40 south to (30,-40)
30 east to (60,-40)
----
Bearing from start = arctan(-40/60) = arctan(-2/3) = -33.69 degrees
------------
Cheers,
Stan H.

Question 994055: If it takes 1.5 days to travel 3,455 kilometers, how fast in mph would they have to travel to make it from new York from Arizona in that time frame?

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What's the distance from NY to AZ?

Question 994016: Mr. Jones Traveled to Ontario on vacation this summer. He traveled 1260 KM in 10.6 hours. What was his average speed?
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To find km/hr, divide the kms by the hours.
-----
What could be more obvious?

Question 994048: Mike made a trip in 40 hours. Joe made the same trip in 30 hours because Joe was traveling 6mph faster than Mike. How many miles was the trip?
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Mike traveled at x mph
He went 40x miles
Joe traveled at x+6 mph
He went 30 (x+6) miles
These are equal
40x = 30x+180, distributing the 30
10x=180
x=18 mph, Mike's speed, and he went 720 miles in 40 hours
x+6=24 mph, Joe's speed, and he went 720 miles in 30 hours

Question 994018: Two planes are 485 mi apart and are traveling toward each other. One plane is traveling 150 mph faster than the other plane. The planes pass each other in 0.5 h. Find the speed of each plane.
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.
Let  u  be the speed of the faster airplane,  in miles per hour  (mph).

Then the speed of the other airplane is  (u-150)  miles per hour.

The equation is

0.5*u + 0.5*(u-150) = 485

(in half an hour airplanes flying toward each other covered the entire distance).

Simplify and solve it:

0.5u + 0.5u - 75 = 485,

u = 485 + 75

u = 560 .

The speed of the faster airplane is 560 miles per hour.

The speed of the other airplane is 560-150 410 miles per hour.

Ques1.
Two drivers, Mike and Peter, travel from Town A to Town B, 112 km away.
They start at the same time and take the same route.
They travel at the average speed of 56 km/h and 64 km/h respectively.
When Peter reaches Town B, how far behind is Mike?
Quest2.
The distance between two town X and Y is 28 km. A car and a lorry leave X at 08.00 to travel to Y. On arriving at Y, the car then returns to X on the same route. When the two vehicles meet, the distance they have travelled are in the ratio 3:5. The average speed of the lorry is 42 km/h.
Calculate
(a) the time at which the two vehicles meet.
(b) the average speed of the car in km/h

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The time that Peter needs to travel from A to B is 112 km/64 km/h=7/4 h.
The time that Mike needs to travel from A to B is 112 km/56 km/h=2h
Peter reaches at B 2-7/4=1/4 h before Mike.
Since Mike travel at the average speed of 56 km/h he will be behind Peter 56km/h*1/4 h= 14 km.

Question 993999: A man intends to run a certain distance in 1/4 th less than he usually takes. By what percentage must he increase his running speed to accomplish this goal?
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Let distance = d and time taken =t
so speed = d/t
New time = (3/4)t
So new speed = d/ (3t/4)
=4d/3t
increase in speed = 4d/3t -d/t
= d/3t
So, percentage increase in speed
=
= 33.33%

Question 993957: Wendy took a trip from city A to city B, a distance of 910 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 30 mi/h, and the train averaged 115 mi/h. The entire trip took
10 1/2h.
How long did Wendy spend on the train?

Found 2 solutions by lwsshak3, josmiceli:
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Wendy took a trip from city A to city B, a distance of 910 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 30 mi/h, and the train averaged 115 mi/h. The entire trip took
10 1/2h.
How long did Wendy spend on the train?
let x=distance Wendy traveled by bus
910-x=distance Wendy traveled by train
distance/speed=travel time
x/30+(910-x)/115=10.5
lcd: (30)(115)
115x+30(910-x)=10.5* (30)(115)
115x+27300-30x=36225
85x=8925
x=105
910-x=805=(distance Wendy traveled by train)
805/115=7
How long did Wendy spend on the train? 7 hrs

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Let = distance in miles she traveled by bus
= distance in miles she traveled by train
Let = time in hrs she spent on bus
= time in hrs she spent on train
-----------------------------------------
Equation for bus:
(1)
Equation for train:
(2)
-----------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
and

Wendy spent 7 hrs on the train
--------------------------
check:
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK

Question 993871: You are trying to swim as many laps as your friend did. After 10 minutes, you have 25 laps left. After 15 minutes, you have 15 laps left. How many laps did your friend swim? How much longer will it take you?
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You are trying to swim as many laps as your friend did.
After 10 minutes, you have 25 laps left.
After 15 minutes, you have 15 laps left.
How many laps did your friend swim?
How much longer will it take you?
:
let x = the number of lap your friend swam
:
10 min 25 laps left
15 min 15 laps left
It took you 5 min to swim 10 laps, therefore 2 laps/min is your speed
:
x - 25 = 10(2)
x - 25 = 20
x = 20 + 25
x = 45 laps swam by your friend
;
your total time to swim 45 laps
45/2 = 22.5 min
:
How much longer will it take you? Assume this means after the 15 min point
22.5 - 15 = 7.5 min to finish

Question 993864: Two trains of length 55 metres and 65 metres travel in opposite directions with speed 70 km/hour and 50 km/hour respectively. Find the time taken for them to completely cross one another.
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Two trains of length 55 metres and 65 metres travel in opposite directions with speed 70 km/hour and 50 km/hour respectively.
Find the time taken for them to completely cross one another.
:
The relative speed between the two trains: 70 + 50 = 120 km/hr
Change 120 km/hr to meters/sec
= 33 meters per sec
:
Find the no. of seconds to travel 55 + 65 = 120 meters
= 3.6 seconds

Question 993954: Christie pilots her plane for 300 mi against a headwind in 2 hrs. The flight would take 1 hr and 30 mins with a tailwind of the same speed. Find the Headwind and the speed of the plane in still air.
The speed of the headwind on the plane is ___mph and the speed of the plane in still air is ___mph.

Found 2 solutions by Boreal, Alan3354:
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plane's speed in calm air=x
wind speed=w
x-w=150 ;; 300 miles in 2 hours is 150 mph
For x+w, we know that 300 miles is done in 3/2 hours. That is 200 mph.
Therefore
x-w=150
x+w=200
2x=350
x=175 mph, speed of plane in still air.
wind speed is 25 mph (headwind/tailwind)

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Christie pilots her plane for 300 mi against a headwind in 2 hrs. The flight would take 1 hr and 30 mins with a tailwind of the same speed. Find the Headwind and the speed of the plane in still air.
----------------
find the 2 groundspeeds, upwind and downwind.
The plane's airspeed is the average of the 2.
The windspeed is the difference between airspeed and groundspeed.
============
We don't need this:
The speed of the headwind on the plane is ___mph and the speed of the plane in still air is ___mph.

Question 993953: A man travels 6 hrs on the freeway and the next 3 hrs with a reduced sped of 20 miles per hour on a country rd, if the total miles travel was 543 miles then how what was the speed on the freeway
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speed on freeway = x mph
speed on road is (x-20) mph
6x+(3(x-20)=543
6x+3x-60=543
9x=603
x=67 mph on freeway
=====
check
67*6=402 miles
47*3=141miles. Sum is 543 miles

Question 993921: A women rowed a canoe for 3.8 miles at 12 mi/hr how long was her trip in minuets