Question

Wekesa and Ndinda working together can cultivate a piece of land in 6 days. Wekesa alone can complete the work in 15 days.After the two had worked for 4 days Wekesa withdrew the service. Find the time taken by Ndinda to complete the remaining work.

Answer 1

Let the efficiency of Wekesa be W and the efficiency of Ndinda be N.

From the given information, we know that:
6(W + N) = 1 (the whole work is completed in 6 days by both Wekesa and Ndinda)

Also, we know that:
15W = 1 (Wekesa can complete the work in 15 days)

After working for 4 days, the amount of work completed by Wekesa and Ndinda together would be:

4(W + N) = 4/6 = 2/3

So, the amount of work left to be done is 1 - 2/3 = 1/3

Since Wekesa alone can complete the work in 15 days, his daily efficiency is 1/15.

The amount of work completed by Wekesa in 4 days is:
4 x 1/15 = 4/15

Therefore, the amount of work left for Ndinda to complete is:
1/3 - 4/15 = 5/15 - 4/15 = 1/15

Ndinda's daily efficiency N can be calculated as:
6(W + N) = 1
6(1/15 + N) = 1
1/15 + N = 1/6
N = 1/6 - 1/15
N = (5 - 2)/30
N = 3/30
N = 1/10

Since Ndinda's daily efficiency is 1/10, it will take her:
1/(1/10) = 10 days

Therefore, it will take Ndinda 10 days to complete the remaining work after Wekesa withdrew his service.