SOLUTION: The distance between two cities A and B is 140 km. A car driving from A to B left at the same time as a car driving from B to A. The cars met after one hour, then the first car r

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Question 1185921: The distance between two cities A and B is 140 km. A car driving from A to B left at the
same time as a car driving from B to A. The cars met after one hour, then the first car reached
city B 35 minutes later than the second car reached city A. Find the speed of the car from city
A to B.

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.
The distance between two cities A and B is 140 km. A car driving from A to B left at the
same time as a car driving from B to A. The cars met after one hour, then the first car reached
city B 35 minutes later than the second car reached city A. Find the speed of the car from city A to B.
~~~~~~~~~~~~~~~ 

Let  "a"  be the speed of the car A, in km/h;

let  "b"  be the speed of the car B, in km/h.


Then you have these two equation


    a + b = 140  kilometers           (1)     (The cars met after one hour)

    140%2Fb - 140%2Fa = 35%2F60  of an hour    (2)    (first car reached city B 35 minutes later than the second car reached city A)


From the first equation, express b = 140-a  and substitute it into the second equation.  You will get then


    140%2F%28140-a%29 - 140%2Fa = 7%2F12

    20%2F%28140-a%29  - 20%2Fa = 1%2F12


At this point, I just can to guess the solution  MENTALLY :  a = 60 km/h.


An alternative way is to reduce the last equation to the standard quadratic equation form and solve it formally.


ANSWER.  The speed of the car A is 60 km/h.


CHECK.   a) the speed of the car B is then 140-60 = 80 km/h.

         b) the time equation (2) is then  140%2F80 - 140%2F60 = 7%2F4 - 7%2F3 = %287%2A4%29%2F12+-+%287%2A3%29%2F12 = 7%2F12 = 35%2F60 = 35 minutes.

            ! Correct !

Solved.