# Math

I need help please.

Laurie left home and ran to the lake at 10 mi/h. she ran back home at 8 mi/h. If the entire trip took 27 minutes, how far did she run in all?

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1. She averaged 9 mph.

27 / 9 = 3 miles

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Ms. Sue
2. d = r t ... t = d / r

27/60 = (d / 10) + (d / 8)

54/120 = (12 d / 120) + (15 d / 120)

d is the distance to the lake

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3. the trip times are not the same, so the average speed is not 9 mph

sorry, Ms. Sue

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4. Oops! Thanks for catching that, Scott.

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Ms. Sue
5. I agree with Scott

time for first leg = d/10
time for return leg = d/8
total time = d/10 + d/8 = 9d/40

avg rate = total distance/total time
= 2d/(9d/40) = 2d(40/9d) = 80/9 mph

distance = (27/60)(80/9) = 4 miles
So she ran 4 miles in total.

check: 2 miles at 10 mph = 2/10 hrs
2 miles at 8 mph = 2/8 miles
total time = 2/10 + 2/8
= 1/5 + 1/4 = 9/20 hrs = 27 minutes.

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6. why is it 9d/40??

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