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It takes Erica 50 min to drive to work in the morning. She drives home using the same route,
but it takes 21 min longer, and she averages 16 mi/h less than in the morning. How far does Erica drive to work?
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Solution
Let "d" be the one way distance, in miles (the value under the problem's question).
Driving to work is 50 minutes; the average rate is miles per minute.
Driving back is 71 minutes; the average rate is miles per minute.
The difference of the average rates is - miles per minute.
According to the condition, this difference is 16 miles per hour, or miles per minute.
So, you have this equation
- = .
To solve it, multiply both sides by 50*71*60. You will get
60*71*d - 60*50*d = 16*50*71
(60*71 - 60*50)*d = 16*50*71
d = = 45.079.
ANSWER. One-way distance is 45.079 miles.
Solved.