Question

Three students have started a fence-painting business. Working together, Pragnesh and Qazi can paint the fence in 12 hours. Similarly, Pragnesh and Ronghui can paint the fence in 15 hours when they work together. Finally, when Qazi and Ronghui work together, they can paint the fence in 20 hours. How many hours would it take if all three students worked together to paint the fence?

Answer 1

Explanation:

P and Q can do the whole work in 12 hours.

so, in 1 hour they can do 1/12.

P and R can do in 1 hour 1/15.

Q and R can do in 1 hour 1/20.

mathematically that looks like

P + Q = 1/12

P + R = 1/15

Q + R = 1/20

P + Q + R = 1/x

together they can do 1/x of the work in 1 hour.

it will take them x hours, if all 3 worked together.

from the first equation we get

P = 1/12 - Q

that gives us in the second equation

1/12 - Q + R = 1/15

R = 1/15 - 1/12 + Q = 4/60 - 5/60 + Q = Q - 1/60

but from the 3rd equation we get also

R = 1/20 - Q

so,

Q - 1/60 = 1/20 - Q

2Q = 1/20 + 1/60 = 3/60 + 1/60 = 4/60

Q = 2/60 = 1/30

R = Q - 1/60 = 2/60 - 1/60 = 1/60

P = 1/12 - Q = 1/12 - 2/60 = 5/60 - 2/60 = 3/60 = 1/20

so, we get for the sum :

P + Q + R = 3/60 + 2/60 + 1/60 = 6/60 = 1/10

that means in 1 hour they can do together 1/10 of the work.

so, together they will need 10 hours to paint the fence.