SOLUTION: Peter drove to work at 40 miles per hour and arrived one minute late. If he had driven at 45 miles per hour, he would have arrived one minute early. How far does Peter drive to wor

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Question 5087: Peter drove to work at 40 miles per hour and arrived one minute late. If he had driven at 45 miles per hour, he would have arrived one minute early. How far does Peter drive to work? Please explain and solve.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Of course the basic formula for this is D= RT.

Let t= time (in hours) required to arrive ON TIME
Change 1 minute early or late to 1%2F60 hour early or late.
t%2B+1%2F60 = time required to arrive a minute late at 40 mph.
t+-+1%2F60 = time required to arrive a minute early at 45 mph.
Distance is the same either way he arrives, so RT = RT
40%28t+%2B+1%2F60%29+=+45+%28t-+1%2F60%29+

Use distributive property to remove the parentheses:
40t+%2B+40%2F60+=+45t+-+45%2F60+

Subtract 40t from each side:
40t+-+40t+%2B+40%2F60+=+45t-+40t++-+45%2F60+
+40%2F60+=+5t+-+45%2F60+

Add 45%2F60 to each side:
40%2F60+%2B+45%2F60+=+5t+-+45%2F60+%2B45%2F60
85%2F60+=+5t+

Divide both sides by 5:
17%2F60+=+thours. (This means 17 minutes to arrive ON TIME!)

Distance = Rate * Time
(At 40) 40%2A18%2F60= 12 miles, arriving 1 minute late.
(At 45) 45%2A16%2F60= 12 miles, arriving 1 minute early.

Calculating distance both ways is a check!!

R^2 at SCC