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
Pablocito
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

A08
Jul 26, 2017

Using the kinematic expression for constant velocity

#s = v t#

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 = 75 t # ....(1)

2nd train

#s = 105 ( t-2)# .....(2)

Eliminating #t# from these equations. From equation (1)

#t=s/75#

Inserting this value in (2)

#s = 105 ( s/75-2)#
#=>s = 105 ( (s-150)/75)#
#=>5s = 7 ( s-150)#
#=>2s = 7 xx150#
#=>s = 7 xx150/2#
#=>s = 7 xx75=525 " miles"#

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