Question 1135946
let a = the rate of the older pump.
let b = the rate of the newer pump.


general formula is rate * time = quantity of work


quantity of work = 1 drained pool.


older pump takes twice as long to drain the pool than the newer pump.


that means that the rate of the newer pump is 2 times the rate of the older pump.


that gets you b = 2a.


when they work together, their rates are aqditive.


combined rate = a + b
time = 2
quantity of work = 1


formula of rate * time = quantity becomes (a + b) * 2 = 1


since b = 2a, the formula becomes (a + 2a) * 2 = 1


combine like terms to get 3a * 2 = 1


simplify to get 6a = 1


divide both sides by 6 to get a = 1/6


that's the rate of the older pump.


since b = 2a, then b = 2/6.


that's the rate of the newer pump.


formula of (a + b) * 2 = 1 becomes (1/6 + 2/6) * 2 = 1 which becomes 3/6 * 2 = 1 which becomes 1 = 1 which confirms the solution is correct.


rate * time = quantity for the older pump becomes 1/6 * time = 1.


this results in time = 6.


rate * time = quantity for the newer pump becomes 2/6 * time = 1.


this results in time = 3.


your solution is that it will take the older pump 6 hours to drain the pool by itself.