help with this math problem before 12.12.14? please

Question

8 artists and 12 students can paint a large mural in 10 hours. 6 artists and students can paint it in 14 hours. find the time it would take for 1 student to paint the mural.

 

and can you also explain how you got to the answer 

Answer 1

Let the time it takes an artist to paint a mural be A and the time for a student be S.
It takes less time for 8 artists, in fact it takes A/8 and it takes S/12 for the students.
A/8+S/12=10 hours and A/6+S/6=14 hours.
Multiply the first eqn through by 24 (least common denominator):
3A+2S=240 and the second by 6:
A+S=84. Double this: 2A+2S=168 and subtract the whole eqn from the other one:
(3A+2S)-(2A+2S)=240-168, so:
A=240-168=72 hours. A+S=84, so S=84-A=84-72=12 hours. Therefore, it takes a student 12 hours to paint a mural.

Check: 8 artists take A/8=9 hours and 12 students S/12=1 to paint a mural: 9+1=10 hours.

6 artists take A/6=12 hours and 6 students take S/6=2 hours to paint a mural: 12+2=14 hours.

Comments

wait so it takes 1 student 84 hours to paint one mural? & can you please explain what all the numbers mean like A=240-168=72? and the same for the students.