Question

A woman has to walk a certain distance. She covers the first half at a speed of 5 kmph and the second half at a speed of 8 kmph. If the total time taken by her is 26 minutes, then find the total distance.

• A. $\frac{3}{2}$ km
• B. $\frac{5}{2}$ km
• C. $\frac{8}{3}$ km
• D. $\frac{4}{3}$ km

Answer 1

The correct option is C $\frac{8}{3}$ km

Let the total distance be $x$ km.

She travels the first half at a speed of 5 kmph.
Hence, time taken is $\frac{x}{2}÷5=\frac{x}{10}$ hours.

And, she covers the second half at a speed 8 kmph.
So, time taken is $\frac{x}{2}÷8=\frac{x}{16}$ hours.

Total time taken is 26 minutes. i.e., $\frac{26}{60}$ hours.

$\Rightarrow \frac{x}{10}+\frac{x}{16}=\frac{26}{60}\Rightarrow \frac{16x+10x}{160}=\frac{26}{60}\Rightarrow 26x=\frac{26}{60}\times 160\Rightarrow x=\frac{26\times 160}{60\times 26}\Rightarrow x=\frac{8}{3}\text{km}$

Thus, the total distance she covers is $\frac{8}{3}$ km.