I have a question in a test paper which I have answered but I am confused about the answer.
Edward takes 12 hours to paint a fence. Danny paints 60% faster than Edward. How long does Danny take to paint the fence?
I thought that Danny would take 40% of the time Edward would take, so my answer was 4 hours and 48min. However, the given answer is 7 hours and 30 minutes. How do they get this answer?
Edward takes 12 hours to paint a fence. So each hour he paints $\dfrac{1}{12}$ of the fence. Danny paints $60$% faster; thus each hour Danny paints $(1+0.6)\times \dfrac{1}{12}=\dfrac{2}{15}$ of the fence. Thus the time Danny needs to finish painting is $\dfrac{15}{2}$ hours, or $7$ hours $30$ minutes.