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### Train B Overtakes Train A

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Date: 01/17/2002 at 10:46:15
From: Vickie
Subject: Train problem

Train A leaves the station traveling at 30 miles per hour. Two hours
later train B leaves the same station travelling in the same
direction at 40 miles per hour. How long does it take for train B to
catch up to train A?

Could you just walk me through this?
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```
Date: 01/17/2002 at 11:46:20
From: Doctor Jeremiah
Subject: Re: Train problem

Hi Vickie,

If train A is going 30 miles/hour, then the amount of distance it can
go in a certain time (call it t) is:

30 miles/hour * t hours = 30t miles

The second train starts out 2 hours later, so for it the time it is
travelling is t-2. That menas that train B (going 40 miles per hour)
can go this distance in t-2 hours:

40 miles/hour * (t-2) hours = 40(t-2) miles

The question says that train B catches up with train A (which mean
that they go the same distance), so that means:

30t = 40(t-2)

Solve for t to find the number of hours the trains were travelling.

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Middle School Algebra
Middle School Word Problems

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