Question

A man can do work in 5 hrs. after 2 h 20 min, the man stops working. he is replaced by a woman to complete the work. she does the remaining work in 1 hr 40 mins. if the woman works alone, how much faster will she be than man

Answer 1

Woman will do that work in 3 h 30 mins if she does it alone.

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Answer 2

Answer:

Woman is 60% faster than man.

Step-by-step explanation:

Time taken by a man to do a work = 5 hrs.

work done by man in 5 hr = 1

work done by man in 1 hr = 1/5

work done by man in 2 h 20 min $(2+\frac{20}{60}=\frac{7}{3})$ = $\frac{1}{5}\times\frac{7}{3}=\frac{7}{15}$

Work left to do  = 1 - 7/15 = 8/15

Time taken by women to do 8/15 work = 1 hr 40 min = 1 + 40/60 = 5/3 hr

Time taken by women to do complete work = $\frac{\frac{5}{3}}{\frac{8}{15}}=\frac{5\times15}{3\times8}=\frac{25}{8}=3\frac{1}{8}=3\,hr\:8\,min$

Extra time taken by man to complete the work = 5 - 25/8 = 15/8 = 1 hr 53 min

Converting this into percentage = $\frac{\frac{15}{8}}{\frac{25}{8}}\times100=\frac{15}{25}times100=15\times4=60$  %

Therefore, Woman is 60% faster than man.