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A car runs for 11 hours. For the first 100 km, the car runs with a certain speed and then it increases its speed by 15 km/h to cover the remaining 280 km. How much time (in hours) does it take to cover the first 100 km?
1. 5
2. 7
3. 3
4. 4

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Best answer
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.

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