Question

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

Answer 1

1.5 hours

Explanation:

we know that

1) Martha can paint a room in 2 hours

so

Martha can paint the 100% of the room in 2 hours

Find out what percentage of the room she can paint in an hour

using proportion

`(100\%)/(2)=(x)/(1)\\\\x=100\%/2\\\\x=50\%`

2) Jamie can paint a room in 6 hours

so

Jaimie can paint the 100% of the room in 6 hours

Find out what percentage of the room she can paint in an hour

using proportion

`(100\%)/(6)=(x)/(1)\\\\x=100\%/6\\\\x=16.67\%`

3) In one hour Martha and Jamie can paint

`50\%+16.67\%=66.67\%`

so

using proportion

Find out how long will it take them to paint the 100% room together

`(1)/(66.67\%)=(x)/(100\%)\\\\x=100/66.67\\\\x=1.5\ hours`