Question

SAT Help

Jack can paint a house in 5 days, and Richard can paint the same house in 7 days. Working together, how long will it take them to finish the job?

How do you solve this?

Answer 1

In 7*5 = 35 days, Jack can paint 7 houses.

In 5*7 = 35 days, Richard can paint 5 houses.

So in 35 days, the two of them can paint 12 houses. To paint just one house, they'll need 1/12 the time, or 35/12 = 2 11/12 days.

Explanation:

Answer 2

Well, their speeds are (
`V_1` is Jack's speed, and
`V_2` is Richard's.

`V_1 = (1)/(5) houses/day \\ V_2 = (1)/(7) houses/day \\ V = V_1 + V_2 = (1)/(5)+(1)/(7) = (7+5)/(35) = (12)/(35)`
They, together, can paint 12 houses in 35 days. To get a single house, we only have to calculate
`(35)/(12)` which is very close to 3 (a bit below)