Find one students time

Question

8 artists and 12 students can paint a large mural in 10 hours. 6 artists and 8 students can paint it in 14 hours. Find the time it would take for one student to paint the mural.

Answer 1

280 hours.

 

let x = rate at which an artist can paint a mural, that is x murals per hour and y= rate at which a student can paint a mural.

 

Then, 8*x + 12*y = 1/10, in other words, the combined effort was 1 mural per 10 hours, or 1 tenth of a mural per hour.

 

Also, 6*x + 8*y = 1/14. Do the math for simultaneous equations and you  get y = 1/280, or 1 mural per every 280 hours. An artist can do it twice as fast, or 1 mural per 140 hours.

 

One artist and 2 students working together could produce a mural in 70 hours.

Two artists and 4 students working together could produce a mural in 35 hours.

Four artists and 8 students working together could produce a mural in 17.5 hours.  Add two more artists and they can produce it in 14 hours. That makes sense, doesn't it?