Math Algebra Grade 7

Question

Tofer and Rei share a room together. They want their room repainted. If Tofer can paint it alone in two hours while Rei can do it in four hours, how long will it take them to paint the room together?

Answer 1

The easiest way to solve this type of problems is to throw in some realistic numbers. Let us say that to paint the room the boys need 4 cans of paint.

If Tofer is able to paint the room in 2 hours, he is using 2 cans per hour. If Rei is able to paint the room in 4 hours, he is using 1 can of paint per hour.

Together Tofer and Rei are using 3 cans of paint per hour.

After the first hour there will be 1 can of paint left. It will take the boy another 20 minutes to finish their work.

Total time is 1 hour 20 minutes.

Alternatively, one can use Algebra

Tofer’s rate of work = room/2 hours = 0.5 room / hour

Rei’s rate of work = room/4 hours = 0.25 room / hour

Together the boys can paint 0.5 + 0.25 = 0.75 room / hour

time to paint 1 room = (1 room) / (0.75 room / hour) = 4/3 hour = 1 hour 20 minutes