Word problem

Question

Doug and Suzie leave their home at the same time and take the same route. Doug is driving and Suzie is riding her bicycle. Doug drives at a rate which is 9mph slower than three times Suzies rate on her bike. After 2 hoursDoug is 34 miles ahead of Suzie. Find both of their rates.

Answer 1

Let S = Suzie's rate and let D = Dave's rate  

 

Doug is 9 mph slower than 3 times Suzie  ==>  D = 3*S - 9  

 

Note that the difference between Dave's rate and Suzie's rate is  

D - S = (3*S - 9) - S = 2*S - 9  

 

This difference is how much faster Doug is going than Suzie and is the rate at which Doug is moving away from Suzie.  Since Doug is 34 miles ahead after 2 hours he must be moving away from her at 34/2 = 17 mph.  So  

 

2*S - 9 = 17

2*S = 26

S = 13  

 

So D = 3*S - 9 = 3*13 - 9 = 39 - 9 = 30  

 

So Doug is going 30 mph and Suzie is going 13 mph  

 

Check:  30 = 3*13 - 9

            After 2 hours Doug has gone 2*30 = 60 miles and Suzie has gone 2*13 = 26 miles  

           60 - 26 = 34