Problema Solution
Two trains leave towns 1428km apart at the same time and travel toward each other. One train travels 22km/h slower than the other. If they meet in hours, what is the rate of each train?
Answer provided by our tutors
let
x = the rate of the first train
y = the rate of the second train
t = the time of the travel before meeting
one train travels 22 km/h slower than the other:
y = x + 22
since rate = distance/time => distance = time*rate
x*t + y*t = 1428
t(x + y) = 1428
plug y = x + 22 into the last equation
t(x + x + 22) = 1428 divide both sides by t
2x + 22 = 1428 - t
x = (1/2)(1428 - t) - 11 km/h
y = x + 22
y = (1/2)(1428 - t) - 11 + 22
y = (1/2)(1428 - t) + 11 km/h
the rate of the faster train is (1/2)(1428 - t) + 11 km/h.
the rate of the slower train is (1/2)(1428 - t) - 11 km/h.