Chiclet said:

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?

2 hours and 24 minutes

3 hours and 12 minutes

3 hours and 44 minutes

4 hours and 10 minutes

4 hours and 33 minutes

There are two ways to approach this.

The first (and the way they'd want to see if you have to write out your steps).

This is a rate question. So if SR = Sally's Rate of Painting (in houses per hour), JR = John's Rate of Painting (in houses per hour), t = the time they spend painting, and n = number of houses completed in that time:

The formula for this problem would be:

(SR x t) + (JR x t) = n

(Sally's Rate of Painting x Time Painting) + (John's Rate of Painting x Time Painting) = Number of Houses Painted
Now we know:

SR = 1/4 house per hour

JR = 1/6 house per hour

n = 1 hour

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

solve for t:

t/4 + t/6 = 1

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

10t/24 = 1

t=24/10

t=2.4 hours

or 2 hours 24 minutes.

or...............

You could approach this question by working backwards from the answers. Pick an answer and figuring out how many houses will be painted in that time:

For example I'd pick the middle answer and work from there:

so in 3 hours and 44 minutes

Sally paints one house in 4 hours (240 minutes)

so in 3 hours and 44 minutes (224 minutes) Sally will paint 0.93 houses.

John paints one house in 6 hours (360 minutes)

so in 3 hours and 44 minutes (224 minutes) John will paint 0.62 houses.

Add the two together and it would be 1.56 houses.

Too high, so you'd move to a smaller number and try again.