word problem

Question

a wall can be painted in 3 minutes by three men.

the first can could complete it alone in 6 min

the seciond man could complete it alone in 10 min

how man minutes would it take for the third man to finish it alone?

Answer 1

x=# of minutes it takes the third man alone

first man's rate is 1/6 of the job done in 1 minute

second man's rate is 1/10 of the job done in 1 minute

third man's rate is 1/x of the job done in 1 minute

together they paint the wall in 3 minutes

(1/6)(3)+(1/10)(3)+(1/x)(3)=1 (job finished)

(3/6)+(3/10)+(3/x)=1

combine like terms

(3/6)+(3/10)=(1/2)+(3/10)=(5/10)+(3/10)=8/10

(8/10)+(3/x)=1

multiply both sides by 10x

(10x)(8/10)+(10x)(3/x)=(10x)(1)

8x+30=10x

30=10x-8x

30=2x

x=30/2

x=15 minutes for the third man to finish the job alone