Question

A train covers a distance of 800 km with an average speed. It could
have saved 1 hr. 40 min. by increasing the average speed of the train
by 40 km/hr. Find the actual speed of the train.

Answer 1

If the train saves 1 hr 40 min for a distance of 800 km by increasing the average speed by 40 km/hr then the actual speed of the train is 120 km/hr.

Step-by-step explanation:

Required Formula:

• Time taken = [Total Distance] / [Average Speed]

Let the actual average speed of the train be “s” km/hr.

The distance covered by the train = 800 km

The new average speed after increasing by 40 km/hr = [s + 40] km/hr

Therefore,

Time taken with the original average speed = $\frac{800}{s}$ hr

And,

Time taken with the increased average speed = $\frac{800}{s+40}$ hr

According to the question, we have,

$\frac{800}{s} - \frac{800}{s+40} = 1 hr 40 min = 1\frac{40}{60} = 1\frac{2}{3}$

⇒ $\frac{800}{s} - \frac{800}{s+40} = \frac{5}{3}$

⇒ $160 [\frac{s+40-s}{s(s+40)}] = \frac{1}{3}$

⇒ 160 * 40 * 3 = s(s+40)

⇒ s² + 40s = 19200

⇒ s² + 160s – 120s – 19200 = 0

⇒ s(s+160) – 120(s+160) = 0

⇒ (s+160)(s-120) = 0

⇒ s = -160 or 120

Neglecting the negative value

⇒ s = 120 km/hr

Thus, the actual average speed of the train is 120 km/hr.

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Answer 2

Answer:

Step-by-step explanation: