Question

Three students have started a fence-painting business. Working together, Pragnesh and Qazi can paint the fence in 2 hours. Similarly, Pragnesh and Ronghui can paint the fence in 3 hours when they work together. Finally, when Qazi and Ronghui work together, they can paint the fence in 4 hours. How long would it take if all three students worked together to paint the fence.

Answer 1

in about 0.92 hours or 55.2 minutes

Explanation:

The time they take to paint the room:

Pragnesh and Qazi = 2 hours

Pragnesh and Ronghui = 3 hours

Qazi and Ronghui = 4 hours

Meaning, each hour (1) they'll paint:

Pragnesh and Qazi =
`(1)/(2th)` of the room

Pragnesh and Ronghui =
`(1)/(3th)` of the room

Qazi and Ronghui =
`(1)/(4th)` of the room

By summing all their work abilities we can determine how long it would take if all three students worked together to paint the fence, which is:

`(1)/(2) + (1)/(3) + (1)/(4) = (13)/(12th)` of the room each hour. Therefore the whole (1) room would be painted in 1 ÷
`(13)/(12)` =
`(12)/(13) hours` or 0.92 hours or 55.2 minutes (0.92 * 60).