SOLUTION: By car, John travels from a city A to city be in three hours. At a rate that was 20 mph greater than Jones, Peter traveled the same distance than two hours. Find the distance betwe

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Question 1187999: By car, John travels from a city A to city be in three hours. At a rate that was 20 mph greater than Jones, Peter traveled the same distance than two hours. Find the distance between the two cities.
Found 3 solutions by Solver92311, josgarithmetic, MathTherapy:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Distance equals rate times time.

Let represent the distance between the two cities, and let represent the speed of the slower traveler.

So the slower traveler's trip can be modeled by:



since he took 3 hours to complete his trip.

The faster traveler's speed can be represented by because he is going 20 miles per hour faster than the slower guy. Therefore his trip over the same distance can be modeled by:



Since we can say:



Solving for we get:



Then



John

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

From
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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
John, Jones, Peter ?
from city A to city be in three hours?
?? 
PERSON           SPEEDS           TIMES        DISTANCE

J                 r               3            (r)(3)

PETER            r+20             2           (r+20)(2)

If those distances are the same value then 3r=2%28r%2B20%29
-
3r=2r%2B40
r=40
highlight%283%2Ar=120%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

By car, John travels from a city A to city be in three hours. At a rate that was 20 mph greater than Jones, Peter traveled the same distance than two hours. Find the distance between the two cities.
Let D be the distance between the cities

Then John's and Peter's speeds are: matrix%281%2C3%2C+D%2F3%2C+and%2C+D%2F2%29, respectively

We then get the following SPEED equation: matrix%281%2C3%2C+D%2F3%2C+%22=%22%2C+D%2F2+-+20%29

2D = 3D - 120 ----- Multiplying by LCD. 6 

2D - 3D = - 120

Distance between the cities, or