SOLUTION: a train travels 30 miles in 5/6 the amount of time it takes a man to drive a car the same distance. if the rate of the train exceeds the rate of the car by 8 miles per hour, find t

Algebra ->  Finance -> SOLUTION: a train travels 30 miles in 5/6 the amount of time it takes a man to drive a car the same distance. if the rate of the train exceeds the rate of the car by 8 miles per hour, find t      Log On


   

Question 1177601: a train travels 30 miles in 5/6 the amount of time it takes a man to drive a car the same distance. if the rate of the train exceeds the rate of the car by 8 miles per hour, find the rate at which the car is traveling.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
          SPEEDS                       TIME            DISTANCE

TRAIN     30%2F%28%285x%29%2F6%29                   5x/6             30

CAR       30%2Fx                           x               30

DFFRNCE    8

You may see an equation you can form but the variable is the time, x, for the car.


RESULTS
Time for car, x=3%2F4hour;
Train speed, 48 mph;
Car speed, 40 mph

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.


            Having the solution,  as it is written and presented in the post by @josgarithmetic,
            I feel the need to  REWRITE  it from the scratch,

            since his presentation is below any acceptable level. 


Let x be the car's rate, in miles per hour.


Then the car's time traveled is   T%5Bcar%5D = 30%2Fx  hours.


According to the condition, then the train's time traveled is  T%5Btrain%5D = %285%2F6%29%2AT%5Bcar%5D = %285%2F6%29%2A%2830%2Fx%29 = 25%2Fx%29  hours.


Thus the train's rate is  30%2FT%5Btrain%5D = 30%2F%28%2825%2Fx%29%29 = %286x%29%2F5.


We are given  that the difference of rates is 8 miles per hour.  It means


    %286x%29%2F5 - x = 8.


To solve this equation, multiply both sides by 5.  You will get


    6x - 5x = 40

       x    = 40.


Thus the rate of the car is 40 miles per hour.

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Solved and presented in a way,   as  it  SHOULD  be  DONE.