Find the distance that each car travels. Car 1 travels 50/mph; car 2 travels 30mph; traveling duration equal. Car 1 travels 15 miles further than car2

Question

a car traveling 50 miles per hour goes 15 miles farther in the same amount of time as a car traveling 30 miles per hour. Find the distance that each car travels

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  With such problems, one variable is often the same and another variable is related -- this makes it possible to solve the problem.

D = RT
T = R/D

For this problem, T is the same ("traveling duration equal").

       T for Car 1  =  T for Car 2
   T = 50/(x+15) = 30/x         where x=distance Car 2 travels

Cross-multiply:
    50x = 30(x+15)
    50x = 30x + 450      [distribute]
    20x = 450              [subtract 30x from both sides]
      x = 22.5 miles  [Car 2]

   (x+15) = 37.5 miles    [Car 1]

Check:
  Is  50/37.5 = 30/22.5   ?
      50*22.5 = 30*37.5   ?

           1125 = 1125   ?yes
    

Answer 2

We know distance = rate x time

 

distance of car 2 = x

 

distance of car 1 = (x + 15)

 

We are given the rate for each

 

So we know for car 1 that

 

(x + 15) = 50t  where t = time

 

For car 2 we know that

 

x = 30t

 

t = x/30

 

If we plug this into the equation for car 1, we get

 

x + 15 = 50(x/30)

 

x + 15 = 50x/30 = 5x/3

 

Multiply thru by 3 to get

 

3(x + 15) = 5x

 

3x + 45 = 5x

 

2x = 45

 

x = 45/2 = 22.5 mi = distance traveled by car 2

 

car 1 travels (x + 15) = 22.5 + 15 = 37.5 mi