37. 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.
Answers
Answer:
Distance = Speed × Time
360 = s × t
⇒ t = 360 / s
Increased speed of the train can be written as s + 5
New time to cover the same distance = t - 1
(s + 5) × (t - 1) = 360 ....(1)
st - s + 5t - 5 = 360
360 - s + 5(360/s) - 5 = 360 [Since, st = 360 and t = 360 / s]
- s + 1800/s - 5 = 0
- s² + 1800 - 5s = 0
s² + 5s - 1800 = 0
We will solve this quadratic equation by quadratic formula
Comparing s² + 5s - 1800 = 0 with ax2 + bx + c = 0, we get a = 1, b = 5, c = - 1800
b² - 4ac = (5)2 - 4(1)(- 1800)
= 25 + 7200
= 7225 > 0
Hence, the real roots exist.
x = [-b ± √ (b2 - 4ac)] / 2a
s = (- 5 ± √ 7225) / 2
s = (- 5 ± 85) / 2
s = (- 5 + 85) / 2 and s = (- 5 - 85) / 2
s = 80 / 2 and s = - 90 / 2
s = 40 and s = - 45
Speed of the train cannot be a negative value.
Therefore, speed of the train is 40 km /hr.