Nivigmat wrote:

i dont understand why we are taking like this

Wd-Wt = 20 ---(1)

Wn-Wt = 5 ----(2)

Coz I wrote this step like (1/Wd)- (1/Wt)= 1/20

similarly 1/Wn - 1/Wt = 1/5

i dont understand when to use 1/x + 1/y and when to take it as x+y

Please explain

Note that Wd is the "time taken by Dave alone".

Also Wt is "time taken by both together"

We are given that Dave takes 20 more hours when he works alone. So Wd = Wt + 20

You use 1/Wd and 1/Wn when working with rates.

The rate of work of Dave = 1/Wd

The rate of work of Diana = 1/Wn

Combined rate of work = 1/Wd + 1/Wn = 1/Wt

The combined rate of work will be more than the rate of work of each person alone.

This is not correct: (1/Wd)- (1/Wt)= 1/20

1/Wt - 1/Wd = 1/Wn ----> We don't know what 1/Wn is. When Dave finishes the rest of the work, he takes 20 hrs. We can't say that Diana takes 20 hrs to finish the work alone.

Another Method:

Instead, say time taken together is T hrs. Dave working alone takes T+20 hrs and Diana working alone takes T+5 hrs.

So 1/(T+20) + 1/(T+5) = 1/T

(Rates are additive)

Here you get T = 10 so time taken by Dave/time taken by Diana = 30/15 = 2/1

Yet another Method:Or think logically

They take T hrs together to complete the work. Dave takes 20 extra hrs because Diana is not working with him. If she were working with him, in T hrs, she would have finished the work that Dave does in 20 hrs.

Time taken by Dave:Time taken by Diana = 20/T

Also, in 5 hrs, Diana completes the work that Dave was doing in T hrs.

So Time taken by Dave:Time taken by Diana = T/5

20/T = T/5

T = 10

time taken by Dave/time taken by Diana = 20/10 = 2/1

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