Probelm Solving linear equations with two variables (using either method)

Question

A train leaves a station and travels east at 90 mph.  Three hours later, a second train leaves on a parallel track east at 140 mph.  When will the second train overtake the first train?

Answer 1

Hello Geoff -

 

This is a classic question. Sometimes the trains are bicycles, if you see what I mean. But not at that speed....

 

Anyway, let x = the distance both trains go to be at the same place, in other words, when the second train overtakes the first.

 

The first train travels for t hours, and at 90 mi/hr. that means 90t = x

The second train travels for s hours, and at 140 mi/hr, and that is 140s = x

 

Now s = t + 3 (three hours later)

 

So we have 90t = x = 140(t + 3)

 

I'll let you solve it the rest of way to get s and t. The overtake time will be t hours after the first train leaves.

 

Hope this helps,

 

Ken