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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 8, 2023
 #1
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D==Distance to the beach.

T ==Time it takes you to drive to the beach at 40 mph

 

D / 40 ==T.....................(1)

D / 50 ==T - 45/60........(2), solve for D, T

 

D==150 miles

Note: If you drive at 50 mph, you would arrive 45 minutes EARLIER and not "later" !!

 Jun 8, 2023
 #2
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t2 - t1 = 0.75

(d / 50) - (d / 40) = 0.75

To solve this equation, let's find a common denominator for the fractions:

(40 * d) / (40 * 50) - (50 * d) / (50 * 40) = 0.75

(40d - 50d) / 2000 = 0.75

(-10d) / 2000 = 0.75

Multiplying both sides by 2000:

-10d = 0.75 * 2000

-10d = 1500

Dividing both sides by -10:

d = 1500 / -10

d = -150

 Jun 9, 2023

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