Question

25. Tom and Jerry must stuff and mail 1000

envelopes for a new marketing campaign. Jerry
can do the job alone in 6 hours. If Tom helps,
they can get the job done in 4 hours. How long
would it take Tom to do the job by himself?
A. 4 hours
B. 5 hours
C. 8 hours
D. 12 hours​

Answer 1

Option D. 12 hours

Explanation:

Let the work done by Tom to do the job alone = x hours

So per hour work done by Tom =
`(1)/(x)`

Jerry can do the job alone in the time = 6 hours

Per hour work done by Jerry =
`(1)/(6)`

Similarly job done by both together in the time = 4 hours

Per hour work done by both together =
`(1)/(4)`

Now we know,

Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry

`(1)/(4)=(1)/(x)+(1)/(6)`

`(1)/(x)=(1)/(4)-(1)/(6)`

`(1)/(x)=(3-2)/(12)`

`(1)/(x)=(1)/(12)`

x = 12 hours

Option D. will be the answer.

Answer 2

12

Explanation:

The general formula for this is

Formula

1/t1 + 1/t2 = 1/t_tot

givens

t1 = 6 hours

t2 = x

t_tot = 4 hours

Solution

1/6 + 1/x = 1/4 Subtract 1/6 from both sides.

1/6-1/6 + 1/x = 1/4 - 1/6 Change to 12 as your common denominator

1/x = 3/12 - 2/12 subtract

1/x = 1/12 Cross multiply

x = 12

Tom would need 12 hours to do the job alone.