Question

1. Martha can paint a room in 2 hours. Jamie can paint the same room in 6

hours. How long, to the nearest tenth of an hour, will it take them to paint
the room together?
2. Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. How
long will it take if they paint the room together?
3. Nicole can paint a room in six hours, Alexandra can paint a room in 5 hours,
and Liana can paint a room in 4 If all three work together, how long
will it take them to paint the room?
4. Jake can paint a room in 7 hours, and Karen can paint the same room in 5
hours. How long will it take to paint the room if they work together?

Answer 1

3. 60/37 hours

4. 35/12 hours

Explanation:

3.

Nicole: 1 room in 6 hours; in 1 hour: 1/6 room

Alexandra: 1 room in 5 hours; in 1 hour: 1/5 room

Liana: 1 room in 4 hours; in 1 hour: 1/4 room

Combined in 1 hour:

1/6 + 1/5 + 1/4

When they work together, they paint a room in x hours.

In 1 hour: 1/x room

1/6 + 1/5 + 1/4 = 1/x

10/60 + 12/60 + 15/60 = 1/x

37/60 = 1/x

x = 60/37

Answer: 60/37 hours

4.

Jake: 1 room in 7 hours; in 1 hour: 1/7 room

Karen: 1 room in 5 hours; in 1 hour: 1/5 room

Combined in 1 hour:

1/7 + 1/5

When they work together, they paint a room in x hours.

In 1 hour: 1/x room

1/7 + 1/5 = 1/x

5/35 + 7/35 = 1/x

12/35 = 1/x

x = 35/12

35/12 hours

Answer: 35/12 hours