A car runs for 11 hours. For the first 100 km, the car runs with a cer

1.	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. 52. 73. 34. 4
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.

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. 52. 73. 34. 4

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.