Question

A vehicle travels one fourth of total distance with speed v1 and remaining part with speed v2 then it's average speed in the total journey is

Answer 1

Answer:

4v1v2 / 3v1 + v2

Explanation:

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Answer 2

The average speed in the total journey is $\dfrac{4v_{1}v_{2}}{v_{2}+3v_{1}}$

Explanation:

Given that,

Speed of vehicle in first case = v₁

Speed of vehicle in second case = v₂

Let the total distance is d.

Distance in first case $d_{1}=\dfrac{d}{4}$

Distance in second case $d_{2}=d-\dfrac{d}{4}$

$d_{2}=\dfrac{3d}{4}$

We need to calculate the time in first case

Using formula of time

$v_{1}=\dfrac{d_{1}}{t_{1}}$

$t_{1}=\dfrac{d_{1}}{v_{1}}$

Put the value into the formula

$t_{1}=\dfrac{\dfrac{d}{4}}{v_{1}}$....(I)

We need to calculate the time in second case

Using formula of time

$t_{2}=\dfrac{d_{2}}{v_{2}}$

Put the value into the formula

$t_{2}=\dfrac{\dfrac{3d}{4}}{v_{2}}$....(II)

We need to calculate the average speed in the total journey

Using formula of average speed

$v_{av}=\dfrac{D}{T}$

Where, D = total distance

T = total time

Put the value into the formula

$v_{av}=\dfrac{d_{1}+d_{2}}{t_{1}+t_{2}}$

Put the value into the formula

$v_{av}=\dfrac{\dfrac{d}{4}+\dfrac{3d}{4}}{\dfrac{\dfrac{d}{4}}{v_{1}}+\dfrac{\dfrac{3d}{4}}{v_{2}}}$

$v_{av}=\dfrac{4v_{1}v_{2}}{v_{2}+3v_{1}}$

Hence, The average speed in the total journey is $\dfrac{4v_{1}v_{2}}{v_{2}+3v_{1}}$

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Topic : average speed

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