+769 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?
+1277
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
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