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.

Respuesta :

Answer:

in about 0.92 hours or 55.2 minutes

Step-by-step 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  =  [tex]\frac{1}{2th}[/tex] of the room

Pragnesh and Ronghui = [tex]\frac{1}{3th}[/tex] of the room

Qazi and Ronghui = [tex]\frac{1}{4th}[/tex] 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:

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