Question

Two trains depart at the same time from the same station and travel in opposite directions. One train travels 25 mph faster than the other train. After 2 hours the trains are 162 miles apart. Find the speed of each train.

Answer 1

Using algebra:
let x=speed of slower train
then x+25 = speed of faster train
After two hours, total distance travelled:
2(x + x+25) = 162 miles
divide by two to get
2x+25 = 81
2x=81-25=56
x=28 mph (slower train, it'd better be half price!)
faster train = 28+25 = 53 mph

Check: (28+53)*2=162 :)

By mental calculations, no pen, paper nor calculator:
Reasoning:
Over two hours, the faster train travelled 50 miles more than the slower. So if both travelled at the slower speed, they would have travelled a total of 162-50=112miles in two hours. Each (of the slower) will have a speed of 112/4=28 mph. The faster one, of course, travels at 28+25=53 mph.