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?
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
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
To find the distance from Boston where the two trains pass each other, we need to determine the time it takes for the passenger train to catch up to the freight train.
Let's calculate the time it takes for the passenger train to catch up to the freight train:
Let t represent the time it takes for the passenger train to catch up to the freight train.
Since the passenger train starts three hours later than the freight train, it travels for t-3 hours.
Using the formula distance = rate × time, we can calculate the distances traveled by each train.
Distance traveled by the freight train = 24 miles per hour × t hours
Distance traveled by the passenger train = 60 miles per hour × (t-3) hours
Since both trains are meeting at the same point, their distances traveled will be equal:
24t = 60(t-3)
24t = 60t - 180
180 = 60t - 24t
180 = 36t
t = 180 / 36
t = 5
Therefore, it takes 5 hours for the passenger train to catch up to the freight train.
To find the distance from Boston where the two trains pass each other, we can substitute t=5 into the equation for the distance traveled by the freight train:
Distance = 24 miles per hour × 5 hours
Distance = 120 miles
So, the two trains pass each other 120 miles from Boston.
To find the distance from Boston where the two trains pass each other, we first need to determine the travel time of each train.
The freight train departs from Boston at 9AM and is the first to leave. The passenger train departs from Boston at noon, three hours later.
Let's calculate the distance traveled by each train when they meet:
The freight train travels at a speed of 24 miles per hour for 3 hours, so its distance covered is 24 miles per hour multiplied by 3 hours, which equals 72 miles.
The passenger train travels at a speed of 60 miles per hour for the same time, 3 hours, so its distance covered is 60 miles per hour multiplied by 3 hours, which equals 180 miles.
Now, since the passenger train had already traveled 180 miles when they meet, the distance from Boston where the two trains pass each other is 180 miles.