SOLUTION: Josh has 2 leaks in his basement. While waiting for the plumber to come, Josh puts a bucket under each leak. The two buckets have the same capacity. The bucket under the first leas

Question 734236: Josh has 2 leaks in his basement. While waiting for the plumber to come, Josh puts a bucket under each leak. The two buckets have the same capacity. The bucket under the first leask fills in 20 minutes. The bucket under the second leak fills in 35 minutes.
a - Josh's brother takes away one of the buckets and places the one bucket under the 2 leaks. About how long will it take for the one bucket to fill completely?
b - Josh wraps a cloth around the first leak, which cuts the rate of that leak in half. At the same time, it doubles the rate of the second leak. How will this affect the time it takes to fill the bucket?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Josh has 2 leaks in his basement. While waiting for the plumber to come, Josh puts a bucket under each leak. The two buckets have the same capacity. The bucket under the first leask fills in 20 minutes. The bucket under the second leak fills in 35 minutes.
a - Josh's brother takes away one of the buckets and places the one bucket under the 2 leaks. About how long will it take for the one bucket to fill completely?
Let x = time (minutes) it takes
then
x(1/20 + 1/35) = 1
multiplying both sides by common denominator of 700:
x(35 + 20) = 700
x(55) = 700
x = 700/55
x = 12.73 minutes
or
x = 12 minutes and 44 seconds
.
b - Josh wraps a cloth around the first leak, which cuts the rate of that leak in half. At the same time, it doubles the rate of the second leak. How will this affect the time it takes to fill the bucket?
Let x = time (minutes) it takes
then
x((1/2)(1/20) + 2(1/35)) = 1
x(1/40 + 2/35) = 1
multiplying both sides by common denominator of 1400:
x(35 + 80) = 1400
x(115) = 1400
x = 1400/115
x = 12.174 minutes
or
x = 12 minutes and 10 seconds

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