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?
+806
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
.
