# Math

A train leaves the station at noon. The train is 180mi from its destination at 12:45PM and 90mi from the destination at 2:15PM.

1. How far is the station from the destination?

2. At what time will the train reach the destination?

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1. assume that the train travels at a uniform rate.
between 12:45 and 2:15 ---> 1.5 hrs
the train went 90 miles
rate = 90/1.5 or 60 mph

now use a simple ratio, if x is the distance traveled from noon to 12:45
x/.75 = 90/1.5
x = .75(90/1.5) = 45 miles
but the train at this point has 180 miles to go, so
the distance from the station to the destination is 225 miles

time to go 225 miles at 60 mph
= 225/60 =3.75 hr
which would make it 3:45 pm

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posted by Reiny

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