Depth · one concept from first principles · step 2 of 4
Pump A alone can empty a swimming pool in hours, and pump B alone can empty it in hours. Pump B starts pumping water out of the pool at 1 p.m. Partway through, pump A is turned on as well, and together they finish emptying the pool at 5 p.m. At what time was pump A turned on?
With the whole pool as 1, pump A empties 1/8 of it per hour and pump B empties 1/5 per hour.
A pump that needs 5 hours does one fifth of the job each hour.
7.RP.A.1Analyze The UnitsB ran from 1 p.m. to 5 p.m., which is 4 hours.
Looking at B alone avoids splitting the time into two phases.
7.EE.B.3Change Focus Count The ComplementPump B by itself removes of the pool between 1 p.m. and 5 p.m.
B needs equal hours for the whole pool, so each hour it does one of those five equal shares, .
B keeps its own steady rate for all hours whether A is on or not, so its share is .
B's share and A's share together make the whole pool, so A had only left to do.
A had to empty the rest of the pool. Let A run for t hours.
A small share at a slow rate takes a bit over an hour and a half.
7.EE.B.4Convert To Algebra8/5 hours is 1 hour and 3/5 × 60 = 36 minutes. A stopped at 5 p.m., so count back.
A was turned on at 3:24 p.m.
7.EE.B.3Analyze The UnitsLook at the worker who never stopped first; the rest of the job belongs to the one who joined late.
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