Question

Question
train travels 40 km at a uniform speed of 30 kmh. Its average speed after travelling another 40 km is 45 kmh for the whole journey. Its speed in the second half of the journey is?​

Answer 1

Answer:

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Explanation:

ATQ

45km/h=40+40/ 40/30+40/x

45=80/4/3+40/x

45=80/4x+120/3x

45=80×3x/4x+120

45=240x/4x+120

45(4x+120)=240x

180x+5400=240x

5400=240x-180x

5400=60x

5400/60=x

90=x

ex

speed for next half of journey =90km/h

let the speed of the train in later half be x

Time taken to travel later 40 km= 40/x hours

total time taken

total distance = 45

average speed= total time

80 = 45

40 40

+

30 x

40x+1200= 80

X 30x

45

x= 90 kmph

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Answer 2

Given

A train travels 40 km at a uniform speed of 30 kmph

Distance (s) = 40km

Speed (v) = 30kmph

Time taken = s/v = 4/3 hours.

Let, It travels another 40 km at a uniform speed x

Distance (s) = 40km

Speed (v) = x kmph

Time taken = s/v = 40/x hours.

Average speed is the ratio of distance and the time taken to travel it.

Total distance (S) = 80km

Time taken (T) = 4/3 + 40/x

Given, Average speed is 45kmph

$\implies \frac{80}{ \frac{4}{3} + \frac{40}{x} } = 45 \\ \\ \implies \frac{80}{45} = \frac{4}{3} + \frac{40}{x} \\ \\ \implies \frac{16}{9} - \frac{4}{3} = \frac{40}{x} \\ \\ \implies \frac{4}{9} = \frac{40}{x} \\ \\ \implies \: x = 10 \times 9 = 90kmph$

Therefore, The speed of the train in the second half of its journey is 90 kmph.