Rita can cover a distance in 1 hr 24 min by covering two-third of the distance at 4" " km/hr and the rest at 5" " km/hr. Find the total distance?

Correct option is D

Given:
Rita covers two-thirds of the distance at 4 km/hr.
She covers the remaining one-third of the distance at 5 km/hr.
The total time taken is 1 hour and 24 minutes, which is 1.4 hours.
Formula Used:
​$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$​
Solution:
Let the total distance be D  km.
Distance covered at 4 km/hr:
$$\frac{2}{3}D$$​​
Time taken to cover this distance:
$$\text{Time}_1 = \frac{\frac{2}{3}D}{4} = \frac{2D}{12} = \frac{D}{6} \text{ hours}$$​
Distance covered at 5 km/hr:
$$\frac{1}{3}D$$​
Time taken to cover this distance:
$$\text{Time}_2 = \frac{\frac{1}{3}D}{5} = \frac{D}{15} \text{ hours}$$​
Total time taken:
$$\text{Time}_1 + \text{Time}_2 = \frac{D}{6} + \frac{D}{15} = 1.4 \text{ hours}$$​​
$$\frac{5D}{30} + \frac{2D}{30} = 1.4$$​​

$$\frac{7D}{30} = 1.4$$​​
$$7D = 1.4 \times 30$$​​​​
7D = 42
D=6
The total distance is 6 km.