How fast was each plane going?

Question

Two planes left an airport at noon. One flew east at a certain speed and the other flew west at twice the speed. The planes were 2700 mi apart in 3 hours.

Answer 1

let's say the plane that flew east was going at V mi/hr, and the plane that flew west was going at 2V mi/hr.

 

After three hours, the plane that is heading east, is V+V+V miles away from the origin which is 3V miles away from the origin, whereas the plane heading west is 2V+2V+2V miles away from the origin which is 6V miles from the origin.

 

So the distance between the two planes, after three hours,  in terms of variable V would be 6V+3V = 9V miles.

 

 

So 9V=2700 => V= 300 mi/hr  (speed of plane heading east)

 

2V = 600 mi/hr (speed of plane heading west).

 

Now let's check:  

 

300 mi/hr, after three hours it would be 900 mi away from the starting point.

600 mi/hr after three hours it would be 1800 mi away from the starting point (opposite direction as the other plane).

 

So 1800 + 900 = 2700 mi would be the distance between the two planes after 3 hours (as given in the problem).

 

Hope that helps.