Posted by **Zac** on Wednesday, January 26, 2011 at 8:35am.

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

- math -
**Diana**, Wednesday, January 26, 2011 at 8:37am
Sally can paint 1/4 of a house per hour.

John can paint 1/6 of a house per hour.

Let's say the answer is t hours for the total job.

Then (1/4)t + (1/6)t = 1

(1/4 + 1/6)t = 1

(6/24 + 4/24)t = 1

(10/24)t = 1

t = 24/10 hours = 2.4 hours

- math -
**Zac**, Wednesday, January 26, 2011 at 8:51am
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

This is the ans. 2 hours and 24 minutes

But how they work it out?

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**Reiny**, Wednesday, January 26, 2011 at 9:08am
What don't you understand about Diana's solution?

Here is another way to look at it:

Consider the equation: job = rate x time , or rate = job/time or time = job/rate

sally" rate = job/4

john's rare = job/6

combined rate = job/4 + job/6

= 5job/12

time at that rate = job/(5job/12) = 12/5 - 2.4

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**helper**, Wednesday, January 26, 2011 at 2:52pm
From Diana's solution,

2.4 hrs = 2 hrs 24 min

To convert .4 hrs to minutes, multiply by 60.

.4 hrs * 60 min = 24 min

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