SOLUTION: At a certain place the freeway is directly next to and parallel to the railway line. Two cars on the freeway are travelling in the same direction as the train. The one car is mov

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Question 1143058: At a certain place the freeway is directly next to and parallel to the railway line. Two cars on
the freeway are travelling in the same direction as the train. The one car is moving at 1.5 times
the speed of the other. At a certain instant the drivers of both cars are simultaneously directly
next to the rearmost point of the train. The slower car takes 60 seconds to reach the front point
of the train. The train itself takes 30 seconds to cover a distance equal to its own length. If the
train and the cars each travel at a constant speed, how long will it take the faster car to reach
the front point of the train?
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "r" be the speed of the slower car (in meters per second), 

let  L  be the length of the train (in meters), and

let "v" be the speed of the train (m/s).


The "distance" equation for the slower car is

    60*r = L + 60*v.      (1)


We also are given that  

    L = 30*v;             (2)


hence (substituting (2) into (1) and excluding L)


    60*r = 30v + 60v,   or

    60r  = 90v

    r    = %2890%2F60%29%2Av = %283%2F2%29v.


Then the speed R of the faster car is  

    R = 1.5*r = %283%2F2%29%2A%283%2F2%29%2Ar = %289%2F4%29%2Av.      (3)


The "distance" equation for the faster car is

    T*R = L + T*v     (4)

where "T" is unknown time under the question.


Substitute  R = %289%2F4%29%2Av  from (3)   and  L = 30v  from (2) into equation (4).  You will get

    T%2A%289%2F4%29%2Av = 30v + T*v.


Cancel the factor "v" in both sides.  You will get

    %289%2F4%29%2AT = 30 + T.


Multiply both sides by 4 and simplify to solve for T


    9T = 120 + 4T

    9T - 4T = 120,

    5T      = 120,

     T      = 120%2F5 = 24.


ANSWER.  The unknown time T under the question is 24 seconds.

Solved.


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This problem is of the Physics circle level at an advanced school or at a regional university/college.

So,  I gave only major idea and a mainstream of the solution without explaining  "details"  like
"what is this  DISTANCE  equation . . . "  and  "to which distance does it relate".

I sincerely hope that the person who came with such a problem,  is able to understand it on his  (or her)  own from my solution.