Solve a Formula.

Question

A jet flew from Point X to Point Y at an average speed of 280 mph. Because of head winds, the jet averaged only 260 mph on the return trip. The return trip took 10 minutes longer than the original flight. How many hours was the flight from Point Y to Point X? 

 

There are no numbers in the answer, just variables. It would be awesome if you could explain this instead of just answering because I already know what the answer is, I just don't know how to do it and I need to know. 

Answer 1

The formula is Distance = Rate times Time 

 

The Distance is the same each way, call it D 

 

Let T be the time in hours from X to Y 

Then T + 1/6 is the time in hours from Y to X  (10 minutes = 1/6 hour) 

 

D = 280*T                                        is the equation from X to Y 

D = 260*(T + 1/6) = 260*T + 130/3  is the equation from Y to X  

 

Subtract the bottom equation from the top one to get 

 

0 = 20*T - 130/3

20*T = 130/3

T = 130/60 = 2 and 10/60 = 2 hours and 10 minutes from X to Y

 

So T + 10 minutes = 2 hours and 20 minutes from Point Y to Point X 

 

Check:  D = (280 mph)*(13/6 h) = 606 and 2/3 miles  from X to Y

            D = (260 mph)*(14/6 h) = 606 and 2/3 miles from Y to X