Math word problems help? 10 points?

1.) In one hour the first pipe can fill 1/6 of the pool, and in one hour the second

pipe can fill 1/9 of the pool. So in one hour the two pipes working together can

fill (1/6) + (1/9) = (3 + 2)/18 = 5/18 of the pool. So it would take 18/5 hours for

the two pipes working together to fill the pool, and thus

(3/4)*(18/5) = 27/10 = 2.7 hours to fill 3/4 of the pool.

2.) In one minute the cold water faucet can fill 1/12 of the sink and the hot water

faucet can fill 1/15 of the sink. Thus together they can fill

(1/12) + (1/15) = (5 + 4)/60 = 9/60 = 3/20 of the sink in one minute.

Now with the drain open, in one minute 1/25 of the sink's capacity can be drained.

So in one minute, with both faucets on and the drain open, we have a net result of

(3/20) - (1/25) = (5*3 - 4)/100 = 11/100 of the sink filled per minute.

Thus the sink will be filled in 100/11 = 9.0909... minutes.

3.) Since time = distance/speed, we have D/R = d/r, or D = (R/r)*d.

1) 1/6 + 1/9 = 5/18

3/4 X 18/5 = 54/20 = 2.7 hours ANSWER

2) 1/12 +1/15 = 9/60

9/60 -1/25 = 45/300- 12/300 = 33/300 = 11/ 100

100/11 = 9.09 minutes ANSWER

3) D / R = d/ r ANSWER

1

x/6 + x/9 = 3/4

(3x + 2x)/18 = 3/4

5x/18 = 3/4

20x = 54

x = 54/20 = 2.7 hours

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2

1/12 +1/15 -1/25 = 1/x

x = 100/11 = 9.09 min

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