Question

Two planes are 1,400 miles apart. They fly towards each other, one at 100 mph and the other at 200 mph. How long does it take the planes to pass each other (round to the nearest hundredth)?

Answer 1

They start 1400 miles apart, and every hour, that distance shrinks by 300 miles (100 from plane 1, 200 from plane 2). So if we divide 1400 miles by 300 miles per hour, that will give the number of hours required to bring the distance down to zero.

Answer 2

Think of the two planes on a number line. Let one plane be at 0 and the other at 1400.

The first one's position (the one going to the right) will be 0+100t after t hours. (since it starts at 0 and rate*time=distance from 0, or its position).

The second plane's position, since it starts at 1400 and goes to the left, decreases (i.e., gets closer to 0) after t hours, so its position is 1400-200t.

Set the two positions equal to each other. 100t=1400-200t, or t=14/3.

And to check, after 14/3 hours, the first plane will be at about 467, and the second plane will be at 467.