Correct Answer - Option 4 : 4
Given:
Total time car runs = 11 hours
Formula used:
Time = Distance/speed
Calculations:
Let the speed of the car initially be x
For the first 100 km car runs with speed = x km/hr
After 100 km car increases speed by 15 km/hr = x + 15
Remaining distance = 280 km
Total time = 100/x + 280/(x + 15)
⇒ 11 = [(x + 15)100 + 280 × x]/[x(x + 15)]
⇒ 11 = (100x + 1500 + 280x )/(x2 + 15x)
⇒ 11(x2 + 15x) = 380x + 1500
⇒ 11x2 + 165x = 380x + 1500
⇒ 11x2 + 165x - 380x - 1500 = 0
⇒ 11x2 - 215x - 1500 = 0
⇒ 11x2 - 275x + 60x - 1500 = 0
⇒ 11x(x - 25) + 60(x - 25) = 0
⇒ (11x + 60)(x - 25) = 0
So, x = - 60/11 or x = 25
Speed can't be negative so, x = 25
Initially speed was 25 km/h
Required time to cover the first 100 km is 100/25 = 4 hours.
∴ It takes 4 hours to cover the first 100 km.