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
Accepted Solution
A:
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