can someone please review this question and more specifically - the way i did it. i need confirmation that i solved the problem correctly. i know there are many many ways of solving rate problems; with respect - @ this point it's too late for me to learn new ways - just hoping an expert can follow the logic below and say whether i stumbled across the answer by accident or whether this is a correct way of solving this problem (note i said "a way" not "THE way"). thanks!
"Faucet 1 working alone can fill a tub in 20 minutes. Faucet 2 working alone can do the same job in 15 minutes. The hole at the bottom of the tub can empty a full tub in 30 minutes. If both faucets are working at their constant rates given above and the hole is not covered, how long does it take to fill an empty tub?"
(a) 5 minutes
(b) 6 minutes
(c) 10 minutes
(d) 12 minutes
(e) 20 minutes
Ok - here is now I did it:
R x T = W
1/3 x 3/1 = 1
1/4 x 4/1 = 1
After accounting for LCD, the combined rate is 7/12. Then we need to subtract 30 minutes (rate = 1/2) which is represented below (6/12).
Combined rate minue rate of loss:
7/12 - 6/12 = 1/12
So now, we're left with the combined rate plus the rate at which the hole is emptying water at 1/12, which means we need 12 minutes in order for the job do be done (see below).
R x T = W
1/12 x 12 = 1
So the answer is 12 minutes. The correct answer is 12 minutes - just want to make sure that I didn't get the correct answer "by accident" (which has happened to me on occasion. Rare, but it does happen.) Thanks again to whoever checks this.
"Faucet 1 working alone can fill a tub in 20 minutes. Faucet 2 working alone can do the same job in 15 minutes. The hole at the bottom of the tub can empty a full tub in 30 minutes. If both faucets are working at their constant rates given above and the hole is not covered, how long does it take to fill an empty tub?"
(a) 5 minutes
(b) 6 minutes
(c) 10 minutes
(d) 12 minutes
(e) 20 minutes
Ok - here is now I did it:
R x T = W
1/3 x 3/1 = 1
1/4 x 4/1 = 1
After accounting for LCD, the combined rate is 7/12. Then we need to subtract 30 minutes (rate = 1/2) which is represented below (6/12).
Combined rate minue rate of loss:
7/12 - 6/12 = 1/12
So now, we're left with the combined rate plus the rate at which the hole is emptying water at 1/12, which means we need 12 minutes in order for the job do be done (see below).
R x T = W
1/12 x 12 = 1
So the answer is 12 minutes. The correct answer is 12 minutes - just want to make sure that I didn't get the correct answer "by accident" (which has happened to me on occasion. Rare, but it does happen.) Thanks again to whoever checks this.
