Question

Payal can cover a certain distance in $1hr24mins$ by covering two-thirds of the distance at $4km/hr$ and the rest at $5km/hr$. Find the total distance.

• A. $2$ km
• B. $4$ km
• C. $8$ km
• D. $6$ km

Answer 1

The correct option is D $6$ km

Let the total distance be $x$ km.

Speed to cover $\frac{2}{3}xkm=4km/hr$

$\therefore$ time taken $=\frac{\frac{2}{3}x}{4}hr=\frac{x}{6}hr$

Speed to cover $(x-\frac{2}{3}x)$ i.e., $\frac{x}{3}km=5km/hr$

$\therefore$ Times taken $=\frac{3}{5}hr=\frac{x}{15}hr$

Total time $=$ 1 hr 24 mins.

$\Rightarrow (\frac{x}{6}=\frac{x}{15})hr=$ 1 hr 24 min

$\Rightarrow \frac{7x}{30}\times 60min=84$ mins

$\Rightarrow x=\frac{84\times 30}{7\times 60}=6$

$\therefore$ Total distance $=6km$