Question

A train runs first 75 km at a certain uniform speed and next 90 km at an average speed of 10 km/h more than the normal speed. If it takes 3 hours to complete the journey, then how much time will the train take to cover 300 km with normal speed?
1. 5 hours
2. 5 hours 15 minutes
3. 6 hours
4. 5 hours 25 minutes

Answer 1

Correct Answer - Option 3 : 6 hours

Given:

Distance covered by train at a certain uniform speed = 75 km

Distance covered by train at 10 km/h more than the normal speed = 90 km

Total time taken to complet

⇒ e the journey = 3 hours

Formula used:

Time = Total distance ÷ Speed

Calculation:

Let the speed at which it cover first 75 km be x km/hr

Now, according to the question

(75/x) + [90/(x + 10)] = 3 hours

⇒ (75x + 750 + 90x)/(x² + 10x) = 3

⇒ 3x² + 30x = 165x + 750

⇒ 3x² - 135x - 750 = 0

⇒ 3x² - 150x + 15x - 750 = 0

⇒ 3x(x - 50) + 15(x - 50) = 0

⇒ (3x + 15) (x - 50) = 0

⇒ x = 50, -5

As speed can't be in negative, so, speed will be 50 km/hr

Time to cover 300 km = 300/50 hours

⇒ 6 hours

∴ Time to cover 300 km is 6 hours