Stephanie can clean a pool in 1 hour , and Mark can clean the same pool in 1.5 hours. If the rate at which they work together is the sum of their rates working separately, how many minutes should they need to clean the pool if they work together? (1 hr=60 min)
T = t1*t2/(t1+t2) = 1*1.5/(1+1.5) = 0.6h. = 36 Min.
Stephanie cleans at the rate of 1 pools/hr.
Mark cleans at the rate of 1/1.5, or 2/3 pools/hr.
Their combined rate is 5/3 pools/hr
If r is the rate, t is time, and p is the number of pools, then
r = p/t
(5/3pools/hr) = (1 pool)/t
t = 3/5hr
t = 60*3/5 = 36min
36 is the correct answer.
To find out how many minutes Stephanie and Mark need to clean the pool when working together, we need to calculate their combined rate of work.
Stephanie's rate of work is 1 pool per 1 hour, which means she can clean 1/1 = 1 pool per hour.
Mark's rate of work is 1 pool per 1.5 hours, which means he can clean 1/1.5 = 2/3 pool per hour.
To calculate their combined rate of work, we add their individual rates together: 1 + 2/3 = 3/3 + 2/3 = 5/3.
Now we can determine how many minutes they need to clean the pool when working together. Since 1 hour is equal to 60 minutes, their combined work rate is 5/3 pools per 60 minutes.
To determine how long it will take them to clean the pool together, we set up a proportion:
(5/3 pools) / (60 minutes) = 1 pool / x minutes (where x is the time it takes to clean the pool together)
By cross-multiplying, we get: (5/3) * x = (60) * 1
Simplifying, we get: 5x/3 = 60
To solve for x, we multiply both sides of the equation by 3/5: x = (60) * (3/5)
Calculating, we find: x = 36
Therefore, it will take Stephanie and Mark 36 minutes to clean the pool when working together.