Question

Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?

Answer 1

how big is the pool ? \./

Answer 2

it doesnt say.... im trying to study for ged exam :(

Answer 3

You cant answer if i dont know big it is

Answer 4

I mean i could give an approximate answer but thats approximate

Answer 5

You don't need the volume.

Answer 6

Use the combined rates formula:
\[\frac{ 1 }{ Time\ taken\ by\ a }+ \frac{ 1 }{ Time\ taken\ by\ B } = \frac{ 1 }{ Time\ taken\ by\ A\ and\ B\ together }\]

Answer 7

well it says the answer is 15 minutes and here is the reasoning The amount of time it takes the three of them to fill the pool may be represented by the equation, 1/30+1/45+1/90=1/t, where t represents the number of minutes. Solving for t gives t = 15. Thus, after 15 minutes, the three of them will fill the pool, when working together.
i dont understand

Answer 8

I see jim=A
sue=B
tony=C i dont see C

Answer 9

The equation works with any number of people:
\[\frac{ 1 }{ T_A }+\frac{ 1 }{ T_B }+\frac{ 1 }{ T_C }... = \frac{ 1 }{ T_total }\]

Answer 10

number of units produced per minute * number of minutes = number of units produced. the number of units produced is 1 full pool. jim can fill the pool in 30 minutes which means jim can fill 1/30 of the pool each minute. 1/30 * 30 = 1
sue can fill the pool in 45 minutes which means sue can fill 1/45 of the pool each minute. 1/45 * 45 = 1 tony can fill the pool in 1 and 1/2 hours which means that tony can fill the pool in 90 minutes which means that tony can fill 1/90 of the pool each minute. 1/90 * 90 = 1 when they work together, their combined rates are additive.
if we let x = the number of minutes it takes to fill the pool, then we have: rate * x = 1
the combined rate is equal to jim's rate plus sue's rate plus tony's rate. formula becomes: (1/30 + 1/45 + 1/90) * x = 1
1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90 = 1/15.
their combined rate is 1/15 of the pool every minute.
formula becomes: 1/15 * x = 1
multiply both sides of this equation by 15 to get: x = 15
working together, they will take 15 minutes to fill the pool.
in 15 minutes jim has filled 1/30 * 15 = 15/30 = 1/2 of the pool.
in the same 15 minutes, sue has filled 1/45 * 15 = 1/3 of the pool.
in the same 15 minutes, tony has filled 1/90 * 15 = 1/6 of the pool.
1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1 full pool.

the answer should be (15 minutes).