Question

At 9AM, a freight train leaves Boston for NYC, traveling at an average rate of 24 miles per hour. At noon, a passenger train sets out on the same route, traveling at an average rate of 60 miles per hour. How far from Boston do the two trains pass each other?
___ miles

Answer 1

Step One
How far as the slower train traveled in 3 hours?

Formula
d = r* t
r = 24 mph
t = 3 hours
d = ??
d = 24 * 3
d = 72 miles.

Step two
Start the clock at noon when the faster train begins to move. How much time will elapse before the fast train catches the slow one?

d = 60*t  fast train
d = 24*t + 72 slow train The distances are the same so they can be equated..

Step Three
Solve the equation
60t = 24t + 72  Subtract 24t from both sides.
60t - 24t = 72
36t = 72 Divide by 48
t = 72 / 36
t = 2 hours.

How far does the fast train go in 2 hours?
d = r * t
r = 60 mph
t = 2 hours.
d = 60 * 2
d = 120 miles

How far does the slow train go in 2 hours.
r = 24 mph
t = 2 hours
d = 24 * 2
d = 48 miles

But the slow train started out 72 miles ahead of the fast train. It's distance from Boston is 48 + 72 = 120 miles.

Answer: Both trains will meet 120 miles away from Boston <<<<< Answer