Question

Sam goes to the gym for $1\frac{2}{4}$ hours in the morning and he goes for $2\frac{2}{3}$ hours for cycling in the evening. How much time does he spend in gym and cycling?

• A. $\frac{25}{6}$ hr
• B. $\frac{26}{6}$ hr
• C. $\frac{23}{6}$ hr
• D. None of the above

Answer 1

The correct option is A $\frac{25}{6}$ hr

Time spent in gym = $1\frac{2}{4}$ hours

Time spent in cycling = $2\frac{2}{3}$hours

Total time spent in gyming and cycling $=1\frac{2}{4}+2\frac{2}{3}$

Add the whole number and fractional part separately.

Addition of whole numbers $=1+2=3$

Addition of fractional part $=\frac{2}{4}+\frac{2}{3}$

As these are unlike fractions, convert them into the like fractions

Multiplying with 3 in the fraction $\frac{2}{4}$, we get:
$\frac{2}{4}=\frac{2\times 3}{4\times 3}=\frac{6}{12}$

Multiplying with 4 in the fraction $\frac{2}{3}$, we get:
$\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$

Now, add the fractions
$\frac{2}{4}+\frac{2}{3}=\frac{6}{12}+\frac{8}{12}=\frac{6+8}{12}=\frac{14}{12}$

Now, simplify the fraction
$=\frac{2\times 7}{2\times 6}=\frac{7}{6}$

Now, combine both the whole part and the fractional part that equals to 3$\frac{7}{6}$

Now, convert the mixed number into an improper fraction as follows

$3\frac{7}{6}=\frac{3\times 6+7}{6}=\frac{18+7}{6}=\frac{25}{6}$

Hence, total time spent in the gym and cycling is $\frac{25}{6}$ hr