I have a college algebra word problem that I need help solving.

Question

Two planes started at the same time from the same airport and in opposite directions. one flew 60 miles per hour faster that the other. in 5 hours, they were 5300 miles apart. find the rate of each plane, step by step answer. 

Answer 1

For this problem you need to set up a system of equations and solve them together. The first equation relates the distance traveled to the rates and time taken (Distance = Rate x Time):

 

(1) 5x + 5y = 5300               5 hours at rate x and 5 hours at rate y combined to total 5300 miles.

 

For the second equation, we relate the two rates to one another:

 

(2) x = y + 60                   One plane moved at a rate of 60 mph faster than the other.

 

Now substitute (2) into (1) to get:

 

5(y + 60) + 5y = 5300

5y + 300 + 5y = 5300

10y = 5000

y = 500 mph

 

Plug into (2) to get x:

 

x = 500 + 60

x = 560 mph

 

Lastly, check answer in equation (1):

 

5(560) + 5(500) = 5300?

2800 + 2500 = 5300?

5300 = 5300      YAY!

 

One plane flies at 500 mph and the other flies at 560 mph. Hope this helped!