SOLUTION: A truck traveling at 40 kph and a car traveling at 50 kph leave town A at the same time and travel to a second town B. Upon reaching B, the car turn around immediately and traveled

Question 1097760: A truck traveling at 40 kph and a car traveling at 50 kph leave town A at the same time and travel to a second town B. Upon reaching B, the car turn around immediately and traveled the same road toward A. Find the distance between the towns if the car will meet the truck 30 km from town B.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.

Let D be the distance between the cities A and B.


Till the moment of the meeting the car A covered the distance (D + 30) km,
while the truck covered the distance of (D - 30) km. 


Car   A spent  hours to cover the distance (D+30) at the rate 50 km/h.

Truck B spent  hours to cover the distance (D-30) at the rate 40 km/h.


The time spent is the same, which gives you an equation

 = .


To solve it, cross multiply and simplify:

40*(D+30) = 50*(D-30)  ====>

40D + 1200 = 50D - 1500  ====>  1200 + 1500 = 50D - 40D  ====>  10D = 2700  ====>  D =   = 270.


Answer.  The distance between the cities A and B is 270 kilometers.


Check.    = 6 = .   ! Correct !

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