Left on together, the cold and hot water faucets of a certain bathtub take 7 minutes to fill the tub. If it takes the cold water faucet 17 minutes to fill t

Question

Thanks for your help , please do not round 

Answer 1

This question deals with the rates. Let us call the rate for Cold Faucet with R_c whereas that of hot water with R_h. Since the rate of filling the tab with volume V is given by R = V/t, where t is the time to fill it in. We can write for both of them the following:

R_c = V/17
R_h = V/t
R_c + R_h = V/7

where t is the time that we need to find.

V/17 + V/t = V/7

Divide both sides by V to get:
1/17 + 1/t = 1/7

Rearrange:

1/t = 1/7 - 1/17

Bring to common denominator:

1/t = (17 - 7)/(7*17) = 10/119

Take an inverse:
t = 119/10 = 11.9 minutes.

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Answer 2

Let x = number of minutes it takes the hot water faucet to fill the tub alone

 

1/x = portion of tub filled by the hot water faucet per minute

1/17 = portion of tub filled by the cold water faucet per minute

1/7 = portion of tub filled by both faucets per minute

 

Then, 1/x + 1/17 = 1/7

 

119 + 7x = 17x

 

        119 = 10x

 

           x = 11.9 minutes