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

Answer: 55.4 mins

Explanation:

pragnesh and qazi = 2hrs

pragnesh and roghui = 3hrs

qazi and roghui = 4hrs

this means for every 1 hour they wold paint.

pragnesh and qazi =
`(1)/(2)` half of the fence

pragnesh and roghui =
`(1)/(3)`

qazi and roghui =
`(1)/(4)` quarter of the fence

time taken when they all work together

=
`(1)/(2)` +
`(1)/(3)` +
`(1)/(4)`

=
`(13)/(12)`

=
`(12)/(13)`

= 0.9231 × 60(mins)

= 55.4 mins