Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels
12
miles per hour slower than the westbound train. If the two trains are 300 miles apart after 2hours, what is the rate of the westbound train?
Speed:
v = s / t
s = distance
t = time
Distance:
s = v • t
v1 = westbound train speed
v2 = eastbound train speed
The eastbound train travels
12 miles per hour slower than the westbound train, means:
v2 = v1 - 12
s1 = distance the westbound train of station
s2 = distance the eastbound train of station
s1 = v1 • t
s2 = v2 • t = ( v1 - 12 ) • t
The two trains are 300 miles apart after 2 hours so:
t = 2 h
s1 + s2 = 300
v1 • t + ( v1 - 12 ) • t = 300
t • ( v1 + v1 - 12 ) = 300
t • ( 2 v1 - 12 ) = 300
2 • ( 2 v1 - 12 ) = 300
Divide both sides by 2.
2 v1 - 12 = 150
Add 12 to both sides.
2 v1 = 162
v1 = 162 / 2
v1= 81
The rate of the westbound train = 81 mi / h