SOLUTION: You must leave for campus in half an hour, or you will be late for your 8:00 Math class. Unfortunately, you are snowed in. You can shovel the driveway in 45 minutes and your brothe

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Question 277020: You must leave for campus in half an hour, or you will be late for your 8:00 Math class. Unfortunately, you are snowed in. You can shovel the driveway in 45 minutes and your brother claims he can do it in 36 minutes. If you shovel together, how long will it take to clear the driveway? Will this give you enough time before you have to leave?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you can shovel it in 45 minutes.
your brother can shovel it in 36 minutes.
you have to leave in 30 minutes.

you'll make it.

here's why.

rate * time = units

the unit = 1 (the driveway).

your rate is 1/45 meaning you can shovel 1/45 of the driveway in 1 minute.

his rate is 1/36 meaning he can shovel 1/36 of the driveway in 1 minute.

your combined rate * time = 1 driveway.

(1/45 + 1/36) * T = 1

multiply both sides of this equation byh (45*36) to get:

(36 + 45) * T = 36*45*1

simplify to get:

81 * T = 36*45*1

divide both sides of this equation by 81 to get:

T = (36*45*1)/81

Simplify to get T = 20

you'll have 10 minutes to spare.