a group of college students are volunteering for help the homeless during their spring brake. they are putting the finishing touches on a house they built. working alone bill can paint a certain room in 9 hrs. paul can paint the room in 8 hrs. write an equation that can be used to find how long it will take them to paint the room. round if necessary.

Question

whpalmer4 · Answer

brakes are what you use to slow a car.

These problems are usually easily solved if you first figure out the rate at which each worker or machine or pipe or what have you works.  If Bill works along, it takes him 9 hours to paint the room.  Therefore, his rate is 1 room / 9 hours or 1/9 room/hour.

Paul needs 8 hours working alone, so his rate is 1 room / 8 hours or 1/8 room/hour.

Together, Bill and Paul do $\frac{1}8 + \frac{1}9$ of a room each hour.  You have 1 room to paint, so the time they will take is 

$$t = \frac{1\text{ room}}{(\frac{1}{8}+\frac{1}{9})\frac{\text{room}}{\text{hour}}}$$