math
posted by Zac on .
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?

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 
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? 
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 
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