Raghu completes his journey in 15 hours. He covers half the distance at 57 km/h and the rest at 78 km/h. What is the length of the journey (in Km)?

Correct option is C

Given:
Total time taken for the journey = 15 hours
Speed for the first half of the distance = 57 km/h
Speed for the second half of the distance = 78 km/h
Formula Used:
Let the total distance of the journey be D km. The time taken to cover each half of the distance can be calculated using the formula:
​$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$​
Solution:
Let the total distance be D km.
Distance for the first half =$$\frac{D}{2}$$​ km
Time taken for the first half:
$$t_1 = \frac{\frac{D}{2}}{57} = \frac{D}{114} \, \text{hours}$$​
Distance for the second half = $$\frac{D}{2}$$​km
Time taken for the second half:
$$t_2 = \frac{\frac{D}{2}}{78} = \frac{D}{156} \, \text{hours}$$​
Total time taken:
$$t_1 + t_2 = 15 \, \text{hours}$$​
$$\frac{D}{114} + \frac{D}{156} = 15$$​​

$$\frac{D \times 26}{2964} + \frac{D \times 19}{2964} = 15$$​

$$\frac{26D + 19D}{2964} = 15$$​

$$\frac{45D}{2964} = 15$$​​
$$45D = 15 \times 2964$$​​
45D = 44460
D =$$\frac{44460}{45} = 988 \, \text{km}$$

Thus, option (c) is right.