+0  
 
0
1
1
avatar+354 

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?

 Jun 27, 2024
 #1
avatar+943 
0

 

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?   

 

When you go faster you'll get there sooner, so the problem

must actually mean "would have arrived 45 minutes earlier."   

 

Distance  =  Rate • Time    

 

There are two cases:    (1)  D  =  (40)(t)   

                                     (2)  D  =  (50)(t –  45 / 60)   

 

Regarding 45 / 60  -  Since the speed is given in miles per hour, the 45 minutes   

must be converted to hours to keep units consistent.  We could have converted    

the speed to miles per minute, but that would have unnecessarily added tedium.  

 

Since the distance is the same in both cases, set them equal and solve for time.   

 

                                            (50)(t – 45 / 60)  =  (40)(t)   

                                                     50t – 37.5  =  40t    

                                                                10t  =  37.5   

                                                                    t  =  3.75   

 

Substitute t back into case (1)                    D  =  (40)(3.75)   

                                                                   D  =  150    

check answer     

Substitute t back into case (2)                    D  =  (50)(3.75 – 0.75)   

                                                                   D  =  (50(3.00)    

                                                                   D  =  150    

.

 Jun 27, 2024

0 Online Users