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Multiple Rates Word Problem

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Starting at home, Ishaan traveled uphill to the grocery store for 12 minutes at just 15 mph. He then traveled back home along the same path downhill at a speed of 30 mph.

What is his average speed for the entire trip from home to the grocery store and back?

Athena  Mar 3, 2017

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Thank you!! I was worried I had made it more complicated than necessary. Also I said "to the grocery store and back twice " which would be 4 times he traveled it, oops haha.

hectictar  Mar 4, 2017
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His average speed will be the total distance he traveled divided by the total amount of time it took him.

Find his total distance:

12 minutes is 12/60 hours, or 0.2 hours.

He went 15 mph for 0.2 hours, so the distance to the grocery store is 15(0.2) = 3 miles.

He went to the grocery store and back twice so his total distance was 3(2) = 6 miles.

Find his total time:

The first trip was 12 minutes.

He went twice as fast on the second trip so his time will be half as much. 12/2 = 6 minutes.

His total time is 12 + 6 = 18 minutes.

Average speed = 6 miles / 18 minutes

Average speed = 1/3 miles per minute.

Average speed = 20 miles per hour.

hectictar  Mar 3, 2017
edited by hectictar  Mar 3, 2017
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Very nicely explained hectictar

I'd give you more points if I could.  Hopefully Athena will give you some points (stars) too :))

Melody  Mar 4, 2017
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Thank you!! I was worried I had made it more complicated than necessary. Also I said "to the grocery store and back twice " which would be 4 times he traveled it, oops haha.

hectictar  Mar 4, 2017
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Here is another gander

r x t = d

a)  12 x 15 = d

b)  6 x 30 = d

a+b = total distance  AND   (a+b) / time  = rate        [(12 x 15) +( 6 x30) ] / 18 = 20mph

ElectricPavlov  Mar 4, 2017