A train leaves a station and travels north at a speed of 75 mph. Two hours later, a second train leaves on a parallel track and travels north at 105 mph. How far from the station will they meet?

2 Answers
Jul 25, 2017

d = 525 miles, t = 5 hours

Explanation:

Equation for each train is d = v t
1st train d1 = 75 ( t+2 )
2nd train d2 = 105 t
When they meet, d1 = d2
75 ( t+2) = 105 t
Solving => t = 5
d1 = 75 ( 5 + 2 ) = 525 miles
d2 = 105 ( 5 ) = 525 miles

Jul 26, 2017

Using the kinematic expression for constant velocity

s=vt

The trains meet after these have traveled the same distance from the station.
Suppose both meet at time t after first left the station

1st train

s=75t ....(1)

2nd train

s=105(t2) .....(2)

Eliminating t from these equations. From equation (1)

t=s75

Inserting this value in (2)

s=105(s752)
s=105(s15075)
5s=7(s150)
2s=7×150
s=7×1502
s=7×75=525 miles