Question

Jean and Mark are going to fill a pool with 2 different sized hoses. Jean can fill the pool in 8 hours, while Mark can complete it in 12 hours. Their supervisor thinks that the job will take 10 hours to complete if they work together. Explain each step in solving this equation, and determine if the supervisor is correct or not.

Answer 1

If Jean can fill the entire pool in 8 hours, what fraction of the pool can she fill in ONE hour?

Answer 2

1/8

Answer 3

correct.
If Mark can fill the entire pool in 12 hours, what fraction of the pool can he fill in ONE hour?

Answer 4

1/12

Answer 5

correct.

If Jean and Mark work together, in ONE hour they can fill: (1/8 + 1/12) of the pool.

Add the two fractions and simplify.

Answer 6

um i got 1/12

Answer 7

If you add 0 to 1/12 you can get 1/12
but not if you add 1/8 to 1/12

Answer 8

the denominaor is 24 right
and numeraotr is 5

Answer 9

yes. 1/8 + 1/12 = 3/24 + 2/24 = (3+2)/24 = 5/24

So if Jean and Mark work together, in ONE hour they can fill: 5/24 of the pool.
To fill 5/24 of the pool it will take 1 hour
To fill the entire pool it will take 24/5 hours = 4.8 hours (we get 24/5 by flipping the fraction 5/24).

So if Jean and Mark work together, they can fill the pool in 4.8 hours.
Therefore, the supervisor is not correct.

Answer 10

If you comes across similar problems in the future, you can quickly solve it if you remember the following;

If one person can do a hob in 'a' hours and another person can do the same job in 'b' hours, then if they work together, they can do the job in:
\[
\frac{1}{\frac 1a + \frac 1b} \text{ hours} = \frac{a*b}{a+b}\text{ hours.}
\]Here we have: Jean can do in 8 hours and mark can do in 12 hours. Together they can do in \(\huge\frac{12*8}{12+8} = \frac{96}{20} = 4.8\) hrs