Question

A man can walk uphill at the rate of $2\frac{1}{2}$ km/hr and downhill at the rate of $3\frac{1}{4}$ km/hr. If the total time required to walk a certain distance up the hill and return to the starting point was $4$ hours $36$ minutes, then what was the distance he walked up the hill?

• A. $6\frac{1}{2}$ m
• B. $5\frac{1}{2}$ m
• C. $4\frac{1}{2}$ m
• D. $4$ km

Answer 1

The correct option is A $6\frac{1}{2}$ m

Let the total distance walked uphill and downhill be 2x km.

Then, $\frac{x}{2\frac{1}{2}}+\frac{x}{3\frac{1}{4}}=(4+\frac{36}{60})hrs$

$\Rightarrow \frac{2x}{5}+\frac{4x}{13}=4+\frac{3}{5}=\frac{23}{5}$

$\Rightarrow \frac{26x+20x}{65}=\frac{23}{5}$

$\Rightarrow \frac{46x}{25}=\frac{23}{5}$

$\Rightarrow x=\frac{23}{5}\times \frac{65}{46}=6.5km.$