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Three hoses work to fill a tub at at different rate. Hose A and B Updated on: 02 Nov 2015, 12:06
Originally posted by HunterJ on 01 Nov 2015, 20:10.
Last edited by HunterJ on 02 Nov 2015, 12:06, edited 2 times in total.
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74% (01:55) correct 26% (02:40) wrong based on 547 sessions

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Three hoses work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 6/5 of an hour. Hoses A and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?

A. 3/10

B. 2/5

C. 1/2

D. 1

E. 6/5

Edited for accurate solution

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Three hoses work to fill a tub at at different rate. Hose A and B 01 Nov 2015, 20:49
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HunterJ
Three hoses work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 6/5 of an hour. Hoses A and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?

A. 3/10

B. 2/5

C. 1/2

D. 2/3

E. 6/5
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Convert the given time to rate and you will be able to add it up.

Total Rate of A and B = Rate of A + Rate of B = 1/(6/5) = 5/6
Total Rate of A and C = Rate of A + Rate of C = 1/(3/2) = 2/3
Total Rate of B and C = Rate of B + Rate of C = 1/2

Adding all three,
2(Rate of A + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2
Rate of A + Rate of B + Rate of C = 1 tub/hour

Time taken by all three together to fill up the tub is 1 hour.
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Three hoses work to fill a tub at at different rate. Hose A and B 01 Nov 2015, 22:37
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Hi,

Total time is 1 hour.

None of the option choices match the arrived solution.

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Three hoses work to fill a tub at at different rate. Hose A and B 03 Nov 2015, 04:03
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HunterJ
Three hoses work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 6/5 of an hour. Hoses A and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?

A. 3/10

B. 2/5

C. 1/2

D. 1

E. 6/5

Edited for accurate solution
Show more

We have ,in 1 hour when two hose working together can fill the tub as follow:
1/a + 1/b = 1/6/5 of the work
1/a + 1/c = 1/3/2 of the work
1/b + 1/c = 1/2 of the work
=>Get total both sides we got : 2(1/a +1/b +1/c) = 12/6 of the work
or 1/a +1/b +1/c = 6/6=1 of the work
Calculate total amount of time taken when three hoses work together 1/1 = 1

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