Question

A man had to walk a certain distance. He covered one thirds of it at 5 kmph and the remaining distance at 6 kmph. If the total time taken is 40 minutes, then find the total distance.

• A. 3.75 km
• B. 4 km
• C. 5.25 km
• D. 6.5 km

Answer 1

The correct option is A 3.75 km

We know that,
$\text{Speed}=\frac{Distance}{Time}$

Let the distance be $x$.
The man covers one third of it at 5 kmph.
Hence, time taken is $\frac{x}{3}÷5=\frac{x}{15}$ hr.

The remaining distance is $x-\frac{x}{3}=\frac{2x}{3}km$.
The man covers this distance at a speed of 6 kmph.
Hence, time taken is $\frac{2x}{3}÷6=\frac{x}{9}$ hr.

Therefore, the total time taken is
$\frac{x}{15}+\frac{x}{9}$ hr., which is equal to 40 minutes or $\frac{40}{60}$ hr.

Hence,
$\Rightarrow \frac{x}{15}+\frac{x}{9}=\frac{40}{60}$
$\Rightarrow \frac{5x+3x}{45}=\frac{2}{3}\Rightarrow \frac{8x}{45}=\frac{2}{3}\Rightarrow x=\frac{2\times 45}{3\times 8}\Rightarrow x=\frac{90}{24}\Rightarrow x=3.75$

Thus, the total distance is 3.75 km.