Question

Out of every 6 hours, Eva spends $1\frac{2}{3}$ hours cycling, $2\frac{5}{6}$ hours running, and the rest of the time studying. How much time does Eva spend studying?

• A. $\frac{1}{2}h$
• B. $\frac{2}{3}h$
• C. $\frac{1}{6}h$
• D. $1\frac{1}{2}h$

Answer 1

The correct option is D $1\frac{1}{2}h$

Time spent cycling $=1\frac{2}{3}h=\frac{1\times 3+2}{3}h=\frac{5}{3}h$

Time spent running $=2\frac{5}{6}h=\frac{2\times 6+5}{6}h=\frac{17}{6}h$

Time spent cycling + time spent running $=\frac{5}{3}+\frac{17}{6}$

$=\frac{5\times 2}{3\times 2}+\frac{17}{6}$

$=\frac{10}{6}+\frac{17}{6}=\frac{10+17}{6}=\frac{27}{6}$

Time spent studying = 6 - (time spent cycling + time spent running)

$=6-\frac{27}{6}$

6 can be written as $\frac{6}{1}$.

Convert $\frac{6}{1}$ into a like fraction by multiplying both the numerator and the denominator by 6.

$=\frac{6\times 6}{1\times 6}-\frac{27}{6}$

$=\frac{36}{6}-\frac{27}{6}$

$=\frac{36-27}{6}$

$=\frac{9}{6}=\frac{3}{2}$

$=1\frac{1}{2}h$