Question

At noon a train leaves Washington, D.C., headed for Miami, Florida, a distance of 1100 miles. The train travels at a speed of 60 mph. At 1 pm a second train leaves Miami headed for Washington D.C., traveling at 70 mph. At what time will the two trains pass each other?

Answer 1

Let t hours be the number of hours needed for the second train to catch up the first one.

Then the first train is  on the way (t+1) hours.

1. First train travels at a speed of 60 mph (t+1) hours and passes

$60\cdot (t+1)\ m.$

2. Second train travels at a speed of 70 mph t hours and passes

$70\cdot t\ m.$

Since two trains will meet, then

$60\cdot (t+1)=70\cdot t,\\ \\60t+60=70t,\\ \\10t=60,\\ \\t=6\ hours.$

Then they will meet at 7:00 p.m.

Answer: 7:00 p.m.