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Old McDonald purchased a pool with a capacity 100 gallons for his farm. One day, at 1:00 p.m., he placed a hose onto the pool which filled it with water at a rate of 5 gal per hour. After 10 hours, horses and cows started drinking the water at a rate of 2 gal/hr. Five hours after that, Mr. McDonald noticed the animals and placed a second hose in the pool which filled it at a rate of 4 gal/hr. When did Mr. McDonald have himself a pool full of water?

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tarhunbalthazar

I say that it was 15 hours later. Because when he left the first hose in the pool at a rate of 5gph, after 10 hours it was filled with 50 gallons. But with the animals drinking from it the rte drops to 3gph. After 5 hours the pool is filled up with 65 gallons. And when the second hose is added the rate is bumped up to 7gph. And 35 gallons is ll that's left needed to fill the pool, so add 5 more hours to the 10 it took to fill the pool up with 35 more gallons of water.

wegnerkolmp2741o

at 10 hours  there will be 10 * 5 = 50 gallons

at 15 hours there will be 50 +5*5 -2*5 gallons = 65 gallons   (25 added by the hose and 10 lost to the animals)

at 15 hours we add another hose so our input rate is 9 gallons per hour and our output rate is 2 gallons per hour = net input is 7 gallons per hour

we need 100 gallons in the pool and we have 65 gallons at 15 hours so we still need 35 gallons


35/7 =5

so 5 more hours

15 +5 = 20 hours

At 20 hours the pool will be full.


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