What is the speed of the slower plane?

Question

Two planes that are 1400 miles apart are traveling toward each other. One plane is traveling 120 mph faster than the other plane. The planes pass each other in 2.5 hours. 

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.

 

With such problems, there is often:

  (1) something that is the same

  (2) something that is related (so we can solve the problem)

 

Draw a (not-to-scale) picture:

Let x = speed of "other plane"

 

           One plane ->                                    Meet          <-  Other plane        

             (x+120) mph                                                        x mph

  |                                                                 +                                               |

  |< -  -  -  -  d -  -  -  -  -  - total distance = 1400 -  -  -  (1400-d)  -  -  -  >|

Since d=rt,

      r (that is, rate or speed) = d/t

 

What is the same?   The time (t) from start to meet for the two planes.

What is related?  The sum of their distance traveled is 1400 mi.   [note: d + (1400-d) = 1400].

 

Distance for "one plane"    +   distance for "other plane"     =   1400

        (x+120)(5/2)           +       x(5/2)                            = 1400        [note: 2.5=5/2]

        x + 120  + x =  560                 [multiply by 2/5]

        2x = 440

        x = 220 mph

  The speed of the slower plane is 220 mph.

 

Check (very importamt):

   Is   220(5/2) +(220+120)(5/2) = 1400   ?

           550 + 850 = 1400   ?

                1400 = 1400   ?yes