Train B Overtakes Train A

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?

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/