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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 6, 2023
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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?  

 

You mean 45 minutes earlier.  Obviously, if you drive faster, you get there faster.  

 

This problem makes use of

the following relationship:                   Distance = Velocity x Time 

 

                                                           D  =  V • T  

 

case 1                                                 D  =  (40) • (T)  

 

case 2                                                 D  =  (50) • (T – 45)  

 

Since the Distance, D, is the  

same for both cases, let's set       

the "V•T"s equal to each other.             (50)(T – 45)  =  (40)(T)  

 

                                                               50T – 2250  =  40T  

 

Subtract 40T from both sides                  10T – 2250  =  0  

 

Add 2250 to both sides                                       10T  =  2250  

 

Divide both sides by 10                                           T  =  225   (this is in minutes)  

 

Divide minutes by 60 to get hours                           T  =  225 min / 60 min/hr  =  3.75 hours  

 

Plug this T back into original equation                     D  =  (40 mi/hr) • (3.75 hr)  =  150 miles  

.

 Jul 12, 2023

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