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.
We can use fraction to solve this problem. Since Jean can fill the pool in 8 hours and Mark in 12 hours, we can use the formula X/8 + X/12 = 1 where X/8 stands for Jean's job and X/12 for Mark's.
X - total number of hours Jean and Mark can fill the pool
To add the two fractions, we need to have the same denominator which is 24.
The equation will be (3X + 2x) / 24 = 1, which will give us a simplified formula of 5X / 24 = 1.
To get X, we need to multiply 24 to both sides (5X/24 and 1) so that the equation will be 5X = 24. We only need to solve for X, so we will remove 5 from X by dividing it to 24, giving us the equation 5X/5 = 24/5.
The final answer will be X = 24/5 hours or 4.8 hours.
Therefore, the supervisor is incorrect since Jean and Mark can fill the pool in less than 10 hours.
