Question

Two trains start heading toward each other from two cities, the distance between which is 720 km, and meet right in the middle. The second train left 1 hour after the first train, but traveled at a speed 4 km/hour faster than the first train. Find the speed of both trains.

Answer 1

each went 720/2 = 360 km

train 1 time t
train 2 time ( t-2)

train 1 speed v
train 2 speed v+4

360 = v t so t = 360/v
360 = (v+4)(t-2) = vt -2v+4t-8

360 = v(360/v) - 2 v +4 (360/v) - 8
360 = 360 - 2 v + 1440/v - 8
2 v + 8 = 1440/v
2 v^2 + 8 v -1440 = 0
v^2 + 4 v - 720 = 0
v = -29 or + 25
one goes 25 the other 25+4 = 29
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check
t = 360/25 = 14.4 hr
29*12.4 = 360 close enough