Question

if dave works alone, he will take 20 more hours to complete a task than if he worked with Diana. if diana works alone she will take 5 more hours to complete the task than she if she worked with dave. What is the ratio of time taken by dave to that taken by diana if each of them worked alone to complete the task​

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

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