Problem 7.
The two trains travel for the same amount of time, but because their speeds are different, they travel different distances. The two distances add to 450 miles.
distance = speed * time
For the commuter train, you have distance d1, time t, and speed s.
For the express train, you have distance d2, time t, and speed s + 25.
The time is 6 hours, so,
For the commuter train, you have distance d1, time 6, and speed s.
For the express train, you have distance d2, time 6, and speed s + 25.
d = st
Commuter:
d1 = st
Express
d2 = (s + 25)t
Add the equations:
d1 + d2 = st + (s + 25) t
d1 + d2 = st + st + 25t
d1 + d2 = 2st + 25t
d1 + d2 = (2s + 25)t
The two distances add to 450 miles, d1 + d2 = 450, and t = 6.
450 = (2s + 25)(6)
75 = 2s + 25
50 = 2s
s = 25
The commuter train's speed is 25 mph.
The express train's speed is 50 mph.
Check:
distance = speed * time
In 6 hours, the commuter train travels d = 25 mph * 6 hours = 150 miles.
In 6 hours, the express train travels 50 mph * 6 hours = 300 miles.
150 miles + 300 miles = 450 miles.
The distances do add to 450 miles and the speed of the express train is 25 mph faster, so our answer is correct.