A certain highway was being repaired, so it was necessary for the traffic to use a detour. At a certain time, a car and a truck met in this detour which was so narrow that neither the truck nor the car was able to pass. Now, the car had gone three times as far into the detour route as the truck had gone, but the truck would take three times as long to reach the point where the car was. If both the car and the truck can move backward at one third of their forward speed, which of these two vehicles should back up in order to permit both to travel through the detour in the minimum amount of time? Thanks for help.
+36923 Car Truck
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x is where they meet...car has travelled 3/4 and truck has travelled 1/4 (in the opposite direction) (because truck travels at 1/3 speed of car)
time units for car to get to x = 3 for truck to get to x is also 3
time units for car to back up to start to let truck pass = 3 x 3 = 9
time units for car to continue forward to other side = 4
Total time for both vehicles to be clear would then be 9+4= 13 time units from point x start
Time units for truck to get to x = 3
Time units for truck to back up to its origin = 3x3 = 9
Time units for truck to then cross thru detour and clear the ither end = 3x4 = 12
Total time if for both vehicles to clear if TRUCK is the one to back up = 9+12 = 21 time units
SO it is faster if the CAR backs up to the start to let the truck pass and then the car continues on its way across.
