A car travels a distance of 2000 m. If the first half distance is covered at 40km/hour and the second half at velocity v and if the average velocity is 48km/hour, then the value of v is -

Given,
Distance = 2000 m = 2 km                    [converted meter into kilometer]
Average Velocity = 48 km/hour
Velocity to cover the first half distance (1 km) = 40 km/h
Velocity to cover the second half distance = v

To find = v

Solution:
We know that,
$Time=\frac{Distance}{Speed}$

So, putting the value of speed and distance in the above equation, we'll get the time taken by the car to cover the first half distance.
$Time=\frac{1}{40}$

Repeating same as above we'll get the time taken by the car to cover the second half distance.
$Time=\frac{1}{v}$

Now, we know that-
Average $Average\ Speed=\frac{Total\ Distance}{Total\ Time}$
Substituting the given values in the above formula we get-
$48=\frac{2}{\frac{1}{40}+\frac{1}{v}}$
$48=\frac{2}{\frac{v+40}{40v}}$
$\frac{v+40}{40v}=\frac{2}{48}$
$\frac{v+40}{40v}=\frac{1}{24}$
$24(v+40)=40v$
$24v+960=40v$
$40v-24v=960$
$16v=960$
$v=\frac{960}{16}$
$v=60km/h$

Hence, the value of $v$ or the speed of the car in the second half is 60km/h.

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Updated on: 10-Oct-2022

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