#### Question 8: A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

#### Video Explanation

#### Explanatory Answer

Step 1: Frame equations based on the information about speed of train.

Let the speed of the train be s km/hr.

Time taken to cover a distance of 360 km at s km/hr = \\frac{360}{s}) hr

If the speed of the train had been 5 km/hr more, speed of train would be (s + 5) km/hr.

Time taken to cover 360 km @ (s + 5) km/hr = \\frac{360}{s + 5}) hr

Time taken to cover 360 km at (s + 5) km/hr is 1 hr lesser than time taken at s km/hr

i.e., \\frac{360}{s + 5}) = \\frac{360}{s}) - 1

\\frac{360}{s + 5}) - \\frac{360}{s}) = -1

Because s ≠ 0 and s ≠ -5, multiply the equation by (s + 5)s

360(s) - 360(s + 5) = -s (s + 5)

360s – 360s - 1800 = -s^{2} – 5s

s^{2} + 5s - 1800 = 0

##### Step 2: Factorize the quadratic equation to find s

s^{2} + 45s – 40s – 1800 = 0

s(s + 45) – 40(s + 45) = 0

(s + 45) (s – 40) = 0

s = -45 or s = 40

Speed cannot be negative ∴ s = 40 km/hr