How far was the flight from Washington, DC, to LA?

Question

Willa flew from Washington, DC, to Los Angeles for a sales conference. When she flew home from Los Angeles, her plane was diverted to New York City because of bad weather in Washington. The flight to the conference was 239 miles shorter than the flight back, but because the prevailing winds blow west to east the flight back east took 36 minutes less time. The speed of the plane from east to west was 445 mph, and the speed of the plane from west to east was 555 mph. How far was the flight from Washington, DC, to LA? (Hint: First figure out how many hours is equal to 36 minutes.)

Answer 1

Following the problem's hint, we find that 36 minutes = .6 hours. Now we can simply use miles for all of our distances and hours for all of our times.

This is a distance-rate problem, so we need the equation D = RT. Because there are two trips, we will need to use this equation twice.

For the first trip, we get:

D = RT

d = 445*t (letting lowercase d and t be the distance and time of the first trip)

For the second trip, we get:

D = RT

d + 239 = 555*(t - .6)

Now we substitute from the first equation into the second:

445*t + 239 = 555*(t - .6)

I'll let you solve this equation for t. (I get 5.2 hours.) The problem asks for the distance from DC to LA, which is d, so plug the value for t into the equation d = 445*t to get d = 2314 miles.