Extra Challenge Solutions #7

College Algebra

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

7.      A plane flies from Pittsburgh to London at an average speed of 600 mph.  The average speed for the return trip is 500 mph.  What is the average speed for the round trip between Pittsburg and London, and explain why the average speed is not 550 mph?       

Solution:  The basic formula is  from which you can derive:

                       and    

                                    and           

The average speed is NOT 550 mph because the TIME traveled at each speed is not the same.  It will be slightly less than 550 mph because more time was spent traveling at the slower speed.  To determine the average speed, you should let D=distance from Pittsburgh to London.  If you would like to make the problem easier, you could choose any arbitrary distance between two cities, and for convenience choose a multiple of both 500 and 600.  For example, suppose the distance between the cities is arbitrarily 6000 miles.  To find the average speed, you must know the total distance and divide by the total time.

But first, you have to calculate the time that it takes for each part of the trip.

Now, Total Time        =      10 +     12 =       22 hours.

          Total Distance = 6000 + 6000 = 12000 miles.          

  Final Answer:                                  

In the general case, let D = distance.

Now,              Total Time        =       +   

                       Total Distance = 2D      

                                                        where the LCD = 3000

  Final Answer:                          

Alternate Method:  Let x = Average Rate  (This might be easier than the previous explanation!)

Total Time:               +    =  

Total Time:                            +                   =       

Multiply both sides by LCD = 3000x :

                                                  +                   =       

                                  3000x •  +  3000x •  =   3000x • 

Divide both sides by 11D:                    

 Final Answer:                                                              

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