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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 25 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive

 Jul 3, 2023
 #1
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The time difference between driving at 40 mph and 25 mph is 45 minutes, which is 3/4 of an hour. So, the equation for the time you spent driving is:

time = (rate * time_difference) / (rate - new_rate)

Plugging in the known values, we get:

time = (40 mph * 3/4 hours) / (40 mph - 25 mph)

time = 7.5 hours

Since the rate is in miles per hour and the time is in hours, the distance traveled is simply the product of the two:

distance = rate * time

distance = 40 mph * 7.5 hours

distance = 300 miles

Therefore, you drove 300 miles to the beach.

 Jul 3, 2023
 #2
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D==Distance to beach,  T==Time it takes to drive to the beach

 

D/40 = T, 

D/25 = T + 3/4, solve for D, T

 

D==50 miles - distance to the beach.

T==5/4 ==1 hour + 15 minute - time it takes to drive to the beach at 40 mph. 

 Jul 4, 2023

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