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: 55.4 mins

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

pragnesh and roghui = [tex]\frac{1}{3}[/tex]

qazi and roghui = [tex]\frac{1}{4}[/tex] quarter of the fence

time taken when they all work together

= [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{4}[/tex]

= [tex]\frac{13}{12}[/tex]

= [tex]\frac{12}{13}[/tex]

= 0.9231 × 60(mins)

= 55.4 mins

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