Question

John does1/2 piece of work in 3 hours.
Joe does 1/4 of the remaining work in 1 hour
and George finishes remaining work in 5 hour.
How long would it have taken the tree working
together to do the work?​

Answer 1

Answer:

$\frac{30}{11}$ hours.

Step-by-step explanation:

Let us assume that the total work is W.

So, according to the given condition,

John takes 3 hours to complete $\frac{W}{2}$ amounts of work.

⇒John take 1 hour to complete $\frac{W}{6}$ amounts of work.  .....(1)

Now, 1/4 th of the remaining work =$\frac{1}{4}(W-\frac{W}{2})$

                                                         =$\frac{W}{8}$

So, the condition gives that,

Joe takes 1 hour to complete $\frac{W}{8}$ amounts of work.  .....(2)

Now, the remaining work =$(W-\frac{W}{2}-\frac{W}{8})$

                                          =$(\frac{8-4-1}{8})W$

                                           =$\frac{3}{8}W$

Again, by the condition,

George takes 5 hours to complete $\frac{3}{8}W$ amounts of work.

⇒George takes 1 hour to complete $\frac{3}{40}W$ amounts of work.  .....(3)

Now, from statement (1),(2), and (3), when they all work together,

they will take 1 hour to complete $(\frac{W}{6}+\frac{W}{8}+\frac{3W}{40})$ amounts of work.

= $(\frac{20+15+9}{120})W$ amounts of work.

=$\frac{44}{120}W$ amounts of work.

=$\frac{11}{30}W$ amounts of work.

Therefore, if they all work together W amounts of work will be done in

$\frac{30}{11}$ hours.

(Answer)

Answer 2

Answer:

2.7 hours

Step-by-step explanation:

John can do part of work in 3 hours = $\frac{1}{2}$

Remaining work = 1- 1/2 = 1/2

Joe does 1/4 of the remaining work in 1 hour  

Joe does part of work in 1 hour = $\frac{1}{4} \times \frac{1}{2}=\frac{1}{8}$

Now remaining work = $\frac{1}{2}-\frac{1}{8}=\frac{3}{8}$

George  finishes remaining work in 5 hour.

George do part of work in 5 hours = $\frac{3}{8}$

George do part of work in 1 hour = $\frac{3}{40}$

John can do part of work in 1 hour = $\frac{1}{6}$

Together they can do part of work in 1 hour = $\frac{1}{6}+\frac{3}{40}+\frac{1}{8}=\frac{11}{30}$

So, they can do 11/30 part of work in hour = 1

They can do complete work in hour = $\frac{30}{11}=2.7 hours$

So, They can complete work together in 2.7 hours