A passenger train takes 3 hours less for a slow train for a journey of 600 km. If the speed of a slow train be x km / hrs. less than that of fast train . Find the increase speed of train when its usual speed is 40 km / hrs .?

Question

Answer

**Given Information:**

- The distance of the journey is 600 km.
- The slow train takes 3 hours more than the fast train for the same journey.
- The speed of the slow train is x km/hr less than the speed of the fast train.

**Let's consider the speed of the fast train as v km/hr.**

**Calculating Time taken by Fast Train:**
- Time = Distance / Speed = 600 / v = 600v⁻¹ hours

**Calculating Time taken by Slow Train:**
- Time = Distance / Speed = 600 / (v - x) = 600(v - x)⁻¹ hours

**Given that the slow train takes 3 hours more than the fast train:**
- 600(v - x)⁻¹ = 600v⁻¹ + 3

**Solving the Equation:**
- 600(v - x) = 600v + 3v(v - x)
- 600v - 600x = 600v + 3v² - 3vx
- 3v² - 3vx - 600x = 0
- v² - vx - 200x = 0

**Simplifying the Equation:**
- v(v - x) - 200x = 0
- v² - vx - 200x = 0

**Factoring the Equation:**
- (v - 40)(v + 5x) = 0

**Equating each factor to zero:**
- v - 40 = 0 or v + 5x = 0

**Solving for v:**
- v = 40 km/hr (Usual speed of the fast train)

**Calculating the Increase in Speed:**
- Increase in Speed = v - 40 = 40 - 40 = 0 km/hr

Therefore, there is no increase in speed when the usual speed of the fast train is 40 km/hr.

Answer

Solution:-

Let the speed of the slow train be 'x' km/hr and the speed of the fast train be (x+10) km/hr.

Time taken by the slow train to cover the distance of 600 km = (600/x) hours

Time taken by the fast train to cover the distance of 600 km = 600/(x+10) hours.

Now, according to the question.

(600/x) - 600/(x+10) = 3

{600(x+10) - 600x}/x(x+10) = 3

600x + 6000 - 600x = 3{x(x+10)}

6000 = 3x^2 + 30x

3x^2 + 30x - 6000 = 0 Dividing it by 3 we get

x^2 + 10x - 2000

x^2 + 50x - 40x - 2000 = 0

x(x+50) - 40(x+50) = 0

(x-40) (x+50)

x = 40 or x = -50

x = -5 is not possible, the speed cannot be in negative.

So, x = 40

Speed of the slow train is 40 km/hr and the speed of the fast train is 40 + 10 = 50 km/hr.

Similar Class 10 Doubts

A fast train takes 3 hours less than a slow train in travelling 600 km. If the speed of the fast train is 10 km / hr more than the speed of slow train. find the speed of both the trains?

A fast train takes 3 hours less then a slow train for a journey of 600km . If the speed of the slow train is 10km/h less then that of the fast train, find the speed of each train.?

A faster train takes 1 hour less than a slower train for a journey of 200 km if the sped of slower train is 10 km/hr less than that of faster train, find the speed of two trains?

And express train travels 40 km distance at a uniform speed if the speed of train had been 20 km/h more than eight would have taken two hours less for same journey find the speed of train?

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