# John does a work in 6 hours. Silvester does the same work in 4 hours. If they both work together?

In how many hours will they complete the work...........plzzzz show working.........thank u very much

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• John
Lv 7

If John does it in 6 hours, he can complete 1/6 of the job in one hour. Silvester can do 1/4 of the job in an hour.

How long it will take them is their combined work effort = 1/6 + 1/4 = times the time it takes them. And they'll complete ONE whole job.

t*(1/4 + 1/6) = 1. 1/4 + 1/6 = 5/12.

t(5/12) = 1.

t = 12/5 = 2.4 hours or 148 minutes.

John = 1/6 jobs/hr

Silvester = 1/4 jobs/hr

John and Silvester = 1/6 + 1/4 = 5/12 jobs/hr

Time = 12/5 or 2.4 hrs/job

• JG
Lv 5

John's rate is 1/6 of the task per hour

Silvester's is 1/4 of the task per hour

Together they do 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the task per hour.

So it will take 12/5 hours which is 2.4 hours or 2 hours, 24 minutes.

First quantify the word problem.

Rate of work x time = work

RT=W

Find the rate of work for John:

R* 6 hr = 1

R = 1/6

Rate of work for SIlvester.

R*4hr = 1

R= 1/4

Now with both their rates of work, which will remain the same, and the amount of work, which will remain the same, solve for time.

R1T+R2T=W

1/6T+1/4T=1

2/12T+3/12T=1

5/12T=1

12/5 hr = T

2 2/5 hr = 2 hours 24 minutes

• Como
Lv 7

Let work to be done = X units

___________________John______Silvester

rate of work (units/h)___X/6________X/4

Working together , the work done per hour is:-

X/6 + X/4 = 2X/12 + 3X/12 = 5X/12

Time = Work done / rate of work

Time = X / 5X/12 h

Time = 12/5 h = 2 2/5 h = 2h 24 min