Question 1202186: The freight train headed north at 9 a.m. at 40 miles per hour. Two hours later, the express train headed north at 60 miles her hour. What time was it when the express was 20 miles further from the town than the freight?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
the freight train left at 9:00 am
the express train left 2 hours later.
th time for the express train is equal to t.
the time for the freight train is equal to t + 2.
the equation for the freight train is 40 * (t + 2) = d.
the equation for the express train is 60 * t = d + 20.
solve for d in both equations to get:
40 * (t + 2) = d
60 * t - 20 = d
simplify both equations to get:
40 * t + 80 = d
60 * t - 20 = d
subtract the first equation from the second to get:
20 * t - 100 = 0
add 100 to both sides of this equation to get:
20 * t = 100
solve for t to get:
t = 5
this makes t + 2 = 7
the freight train is traveling at 40 miles per hour for 7 hours = 280 miles.
the express train is traveling at 60 miles per hour for 5 hours = 300 miles.
300 - 280 = 20 miles.
the express train has traveled 20 more miles than the freight train.
from 9:00 am, the freight train has traveled 7 hours until 4:00 pm.
from 11:00 am, the express train has traveled 5 hours until 4:00 pm.
the express train has traveled 20 more miles than the freight train at 4:00 pm.
that's your solution.
here's what it looks like in excel.
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
When the express train leaves, the freight train has been traveling for 2 hours at 40 mph, so it is 80 miles ahead of the express train.
To get 20 miles farther from the train than the freight train, the express train needs to make up those 80 miles, plus an additional 20 miles.
The difference between the speeds of the two trains is 20 mph; to make up the 80+20 = 100 miles, the express train needs to travel for 100/20 = 5 hours.
The freight train left at 9am; the express train left 2 hours later, at 11am.
When the express train has been traveling for 5 hours, the time will be 5 hours after 11am, which is 4pm.
ANSWER: 4pm
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