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?
Answers
bobpursley
second train travels at three less hours...
distanceF=24*t
distanceP=60*(t-3)
but the distances are the same, so
24t=60(t-3)
solve for time t
then, distance=24t
distanceF=24*t
distanceP=60*(t-3)
but the distances are the same, so
24t=60(t-3)
solve for time t
then, distance=24t
UnicornGirl#210408
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
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