How do I solve this? I've tried everything i know of!

Question

Ann, Matt and Zack are working for a cleaning company. Together they can clean a house in 2 hours. If Ann does the job alone she can finish it in 5 hours. If Matt does the job alone he can finish it in 6 hours. 

 

How long will it take Ann and Zack together to finish the job?

Answer 1

Ann does 1/5 of the job in 1 hour

Matt does 1/6 of the job in 1 hour

Zack does 1/x of the job in 1 hour (Zack takes x hours to do the job alone)

together they do the job in 2 hours

(1/5)(2)+(1/6)(2)+(1/x)(2)=1

(2/5)+(2/6)+(2/x)=1

multiply both sides by the LCM of 30x

12x+10x+60=30x

22x+60=30x

30x-22x=60

8x=60

x=60/8

x=7.5 hours

Zack does the job alone in 7.5 hours

 

Ann and Zack together...

(1/5)(x)+(1/7.5)(x)=1

multiply both sides by 15

3x+2x=15

5x=15

x=15/5

x=3 hours

Ann and Zack can do the job together in 3 hours