MATH SOLVE

4 months ago

Q:
# 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

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