Question

A man travels equal distances of his journey at 40, 30 and 15 km/hr respectively. Find his average speed for the whole journey.

Answer 1

Hi there!
Here's the answer:

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Method-1:
Direct Formula:
¶¶ Suppose a man covers a certain distance at x kmph and an equal distance at y kmph .
Then the average speed during the whole journey is (2xy)/(x+y) kmph.

¶¶¶ Its extension for 3 speeds x, y and z kmph for same diatance is given by
(3xyz)/(xy+yz+zx).

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Now, using this formula,
Required average speed,
= [(3*40*30*15)/{(40*30)+(40*15)+(30*15)}]
= 24 km/hr.

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Method-2:
• Find time taken to travel 1/nth part of distance, where n is the no. of times of speed change.
• Calculate Average speed using the formula

Average speed = (Total distance traveled) /(total time taken)


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Now,
To the given question,
Time taken to travel 1/3 distance of journey with speed 40 kmph, = (1/3)/40
= 1/120.

Time taken to travel 1/3 distance of journey with speed 30 kmph, = (1/3)/30
= 1/90.

Time taken to travel 1/3 distance of journey with speed 15 kmph, = (1/3)/15
= 1/45.

Total time Taken = (1/120) + (1/90) + (1/45) = 45/1080.

Average speed = (Total distance traveled) /(total time taken)
= 1/(45/1080)
= 24 kmph.


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:)
Hope it helps

Answer 2

Answer:

24

Step-by-step explanation:

avg distance formula=

$\\ = \frac{3}{ \frac{1}{x} + \frac{1}{y} + \frac{1}{z} } \\ = \frac{3}{ \frac{1}{40} + \frac{1}{30} + \frac{1}{15} } \\ = \frac{3}{ \frac{3 + 4 + 8}{120} }$

$\\ \: \: \: \: = \frac{3 \times 120}{15} \\= 24$

Hope it helps u