Rate of work

Question

Mower A can mow the village park in 3 hours and mower B can mow it in 2 hours. At 7 am Mower A began to mow the parkand was joined by Mower B at 7:30 am. At what time was the job completed?

Answer 1

A does the 1/3 of the job in 1 hour

B does 1/2 of the job in 1 hour

mower A started at 7:00 am and was joined by mower B at 7:30 am

in 1/2 hour mower A did (1/2)(1/3)=1/6 of the job

this leaves only 5/6 of the job to be done by both mowers together

x=# hours it takes the mowers together to do the job (what's left of the job)

(1/3)x+(1/2)x=5/6 (that part of the job that is left)

multiply both sides by 6

6(1/3)x+6(1/2)x=6(5/6)

2x+3x=5

5x=5

x= 1 hour

7:30 am plus 1 hour brings you to 8:30 am when the job is completed