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# rates

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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?

Jul 14, 2023

#1
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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 15, 2023