Question

Luke can dig a hole in four days and his friend Steve can dig it in five days how long will it take them to dig the hole together

Answer 1

2
`(2)/(9)` days

Explanation:

Let d = the number of days.

`(1)/(4)` d =
`(1)/(5)`d = 1

`(5)/(20)` d +
`(4)/(20)` d = 1

`(9)/(20)` d = 1 Multiply both sides by
`(20)/(9)`

(
`(20)/(9)`)(
`(9)/(20)`) d = 1(
`(20)/(9)`)

d =
`(20)/(9)` I can break 20 into 9 + 9 + 2

d =
`(9)/(9)` +
`(9)/(9)` +
`(2)/(9)`
`(9)/(9)` = 1

d = 1 + 1 +
`(2)/(9)`

d = 2
`(2)/(9)`