Dane is using two differently sized water pumps to clean up flooded water. The larger pump can remove the water alone in 240min. The smaller pump can remove the water alone in 400min. How long would it take the pumps to remove the water working together? minutes

Question

Dane is using two differently sized water pumps to clean up flooded water. The larger pump can remove the water alone in  240min. The smaller pump can remove the water alone in  400min. How long would it take the pumps to remove the water working together? minutes

Bytelearn · Accepted Answer

Determine rates individually: Determine the rates at which the pumps work individually. The larger pump can remove the water in 240 minutes, so its rate is 1/240 of the water per minute. The smaller pump can remove the water in 400 minutes, so its rate is 1/400 of the water per minute.Add rates for combined rate: Add the rates of the two pumps to find their combined rate. Combined rate = Rate of larger pump + Rate of smaller pump Combined rate = 1/240 + 1/400Calculate combined rate: Calculate the combined rate. To add the fractions, find a common denominator, which is 2400 (the least common multiple of 240 and 400). Combined rate = (10/2400) + (6/2400) Combined rate = (10 + 6) / 2400 Combined rate = 16/2400 Combined rate = 1/150 (simplified by dividing both numerator and denominator by 16)Determine time for removal: Determine the time it takes for the pumps to remove the water working together. If the combined rate is 1/150 of the water per minute, then it will take 150 minutes for the two pumps to remove the water together.Verify solution: Verify the solution. The combined rate should be less than the rate of the faster pump and more than the rate of the slower pump. Since 1/150 is between 1/240 and 1/400, the solution is reasonable.

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