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Narender covered the first one-third of a certain distance with a speed of 10 km/hr, the next 2/5th distance of the total distance he covered with a speed of 20 km/hr and the remaining distance he covered with a speed of 40 km/hr. Then the average speed of Narender for the whole journey is 

Narender covered the first one-third of a certain distance with a speed of 10 km/hr, the next 2/5th distance of the total distance he covered with a speed of 20 km/hr and the remaining distance he covered with a speed of 40 km/hr. Then the average speed of Narender for the whole journey is  Correct Answer <span class="math-tex">\({50 \over 3} \ km/hours\)</span>

Given:

Narender's speed for the first one third = 10 km/hr

Narender's speed for the next 2/5th distance of total distance = 20 km/hr

Narender's speed for the remaining distance = 40 km/hr

Formula used:

Time = Distance/Speed

Average speed = Total distance/Total Time

Calculation:

Let total distance be x

Now the time is taken by Narender to cover the first one third at the speed 10 km/h = (x/3)/10 = x/30 hr

Now the time is taken by Narender to cover the 2/5th of the total distance at the speed 20 km/h = (2x/5)/20 = x/50 hr

Now the remaining distance = x – (x/3) – (2x/5) = 4x/15 km

Now the time is taken by Narender to cover the remaining distance at the speed 40 km/h = (4x/15)/40 = x/150 hr

Total time = x/30 + x/50 + x/150

⇒ Total time = 3x/50

Now by the formula of average speed,

Average speed = x/(3x/50) = 50/3 km/hr

∴ The average speed of Narender for the whole journey is 50/3 km/hr

 

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