SOLUTION: how long does it take to fill a reservoir with the intake pipes a and b, if the reservoir can be filled by a alone in 5 days and by b alone in 3 days

Question 1203286: how long does it take to fill a reservoir with the intake pipes a and b, if the reservoir can be filled by a alone in 5 days and by b alone in 3 days
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
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how long does it take to fill a reservoir with the intake pipes a and b,
if the reservoir can be filled by a alone in 5 days and by b alone in 3 days
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Pipe A fills of the reservoir volume per day. Pipe B fills of the reservoir volume per day. Working together, the two pipes fill = = of the reservoir volume per day. Hence, the two pipes will fill the reservoir in days working together. ANSWER

Solved.

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Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
rate * time = quantity
time for a to fill the reservoir alone is 5 days.
time for b to fill the reservoir a;pme is is 3 days.
quanity is 1 filled reservoir.

formula for a is r * 5 = 1
solve for r to get r = 1/5 for a

formula for b is r * 3 = 1
solve for r to get r = 1/3 for b

when they work together, their rates are additive.
you get (1/5 + 1/3) * t = 1
convert fractions to common denominator to get:
(3/15 + 5/15) * t = 1
combine like terms to get:
8/15 * t = 1
solve for t to get:
t = 15/8.

when they work together, they can fill the reservoir in 15/8 days.

since rate * time = quantity, then:
formula for a becomes 1/5 * 15/8 = 15/40 of the reservoir is filled in 15/8 days.
formula for b becomes 1/3 * 15/8 = 15/24 of the reservoir is filled in 15/8 days.

15/40 = 3/8 of the reservoir filled in 15/8 days.
15/24 = 5/8 of the reservoir filled in 15/8 days.
15/40 + 15/24 = 3/8 + 5/8 = 1 filled reservoir.

this confirms that they both fill the reservoir in 15/8 days when working together.

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