One person paints a room in six hours, another in twelve. Together? Not eighteen, and not nine. These free printable word problems build the one idea that makes work problems tractable: add the rates, not the times.
The mistake everyone makes first is to average or add the times, and the fix is to think in rates instead. A painter who takes six hours does one sixth of the room an hour; the other does one twelfth; together they do a quarter of the room an hour, so the room takes four hours. Turning each time into a per-hour rate is the whole method.
Why this sheet works
Pipes filling and draining a tank are the same problem with a sign. A drain works against the fill, so its rate is subtracted, and a child who has the rate idea handles that without a new rule — the tap adds, the drain takes away, and the net rate gives the time.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
1A tank has two faucets. One fills it alone in 5 hours, the other in 12 hours. Both faucets are opened together.How long will it take to fill the tank?
2A tank is filled by two hoses: alone, one takes 2 hours and the other 11 hours. Both hoses are turned on at the same time.How long will it take the two hoses to fill the tank?
3A tank is filled by two faucets. Working alone, one faucet takes 5 hours and the other 4 hours.With both open, what fraction of the tank is filled in one hour?
4A tank is filled by two pipes. Working alone, one pipe takes 8 hours and the other 7 hours.With both open, what fraction of the tank is filled in one hour?
