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

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.

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