Time and Distance Word Problem

Question

Wilma drove at an average speed of 50 mi/h from her home in City A to visit her sister in City B. She stayed in City B 15 hours, and on the trip back averaged 60 mi/h. She returned home 46 hours after leaving. How many miles is City A from City B

Answer 1

We have to first figure out how many hours she was driving total.  To do that, we take 46-15 = 31 hours. 

 

Let X = number miles from City A to City B.

 

On the trip from City A to City B, to find the number of hours the trip took:

 

X miles *(   1 hr    ) = X/50 hrs

               50 miles

 

On the trip from City B back to City A, to find the number of hours the trip took:

 

X miles *(    1 hr    ) = X/60 hrs
                60 miles

 

The total trip took 31 hours:

 

 X   + X    = 31

50     60

 

Multiply through by 50:

 

X + 50X   = 1550

       60

 

Multiple through by 60:

60X + 50X = 93000

 

110X = 93000

 

X = 845.5 miles