17. Last year's match at Wimbledon between John Isner and Nicolas Malut, which lasted 11 hours and 5 minutes, set a record for the longest match in tennis history. The fifth set of the match lasted 8 hours and 11 minutes.
Approximately what fraction of the whole match was taken up by the fifth set?
A $\frac{1}{5}$
B $\frac{2}{5}$
C $\frac{3}{5}$
D $\frac{3}{4}$
E $\frac{9}{10}$
Solution: D
We have that 8 hours and 11 minutes is $8 \times 60+11=491$ minutes and 11 hours and 5 minutes is $11 \times 60+5=665$ minutes. Therefore the exact fraction taken by the last set is $\frac{491}{665}$. So we need to decide which of the given fractions this is closest to. This can be done in more than one way. For example, as 491 is just below 500 and 665 is almost $\frac{1}{3}$ rds of 2000 , we have that $\frac{491}{665} \sim \frac{500}{\frac{1}{3}(2000)}=\frac{1}{\frac{1}{3}(4)}=\frac{3}{4}$. (Here " $\sim$ " means "is approximately equal to".) Another method is to say that $\frac{491}{665} \sim \frac{490}{665}=\frac{98}{135}=\frac{14}{19} \sim \frac{15}{20}=\frac{3}{4}$.