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1) Amy has two solutions available in the laboratory, one with 5% alcohol and the other with 10% alcohol. How much of each should she mix together to obtain 5 gallons of 8%

2)Beverly can drive 600 miles in the same time as it takes Susan to drive 500 miles. If Beverly drives 10 mph faster than Susan, then how fast does Beverly drive?

3)It takes 10 minutes to fill alishas bathtub and 12 mintues to drain the water out. How long would it take to fill it with the drain accidentally left open?

"Amy has two solutions available in the laboratory, one with 5% alcohol and the other with 10% alcohol."

x gallons of the 5% solution contains 0.05x gallons of alcohol

y gallons of the 10% solution contains 0.10y gallons of alcohol

"How much of each should she mix together to obtain 5 gallons of 8%"

x + y = 5

x = 5 - y

The mixture contains 0.08·5 = 0.4 gallons of alcohol.

0.05x + 0.10y = 0.4

0.05(5 - y) + 0.10y = 0.4

0.05y = 0.15

y = 3

x = 5 - y = 2

Mix 2 gallons of 5% solution with 3 gallons of 10% solution.

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"Beverly can drive 600 miles in the same time as it takes Susan to drive 500 miles."

b = Beverly's speed in miles per hour

s = Susan's speed in miles per hour

distance/rate = time

600/b = 500/s

"If Beverly drives 10 mph faster than Susan, then how fast does Beverly drive?"

s = b - 10

600/b = 500/(b - 10)

600(b - 10) = 500b

b = 60

Beverly drives 60 miles per hour.

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"It takes 10 minutes to fill Alisha's bathtub and 12 minutes to drain the water out."

fill rate = 1 tub per 10 minutes = 1/10 of the tub per minute

drain rate = 1 tub per 12 minutes = 1/12 of the tub per minute

"How long would it take to fill it with the drain accidentally left open?"

net rate = 1/10 - 1/12 = 1/60 of the tub filled per minute

It takes 60 minutes = 1 hour to fill the tub.

Word Problems

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