Question

A car moves along a straight road. It covers first half distance with speed

36km/h and remaining half distance with 48km/h. Calculate the average speed of

the car ​

Answer 1

Answer:

41.14 km/h

Explanation:

As per the provided information in the given question, we have :

• Car covers first half distance with speed 36km/h.
• And, remaining half distance with 48km/h.

We are asked to calculate average speed of the car.

Average speed formula :

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }} }$

★ Calculating total distance :

Let us assume the first half distance as d km, and second half distance will also be d km. So,

$\longmapsto \rm { Distance_{(Total)} = Distance_{(1st \; half)} + Distance_{(2nd \; half)} }$

$\longmapsto \rm { Distance_{(Total)} = (d + d) \; km }$

$\longmapsto \rm { Distance_{(Total)} = 2d \; km }$

∴ Total distance travelled is 2d km.

★ Calculating total time :

$\longmapsto \rm { Time_{(Total)} = Time_{(1st \; half)} + Time_{(2nd \; half)} }$

$\longmapsto \rm { Time_{(Total)} = t_1 + t_2 }$

• Time = Distance/Speed

$\longmapsto \rm { Time_{(Total)} =\Bigg ( \dfrac{d}{36} + \dfrac{d}{48}\Bigg ) \; h}$

$\longmapsto \rm { Time_{(Total)} =\Bigg ( \dfrac{4d + 3d}{144}\Bigg ) \; h}$

$\longmapsto \rm { Time_{(Total)} =\Bigg ( \dfrac{7d}{144}\Bigg ) \; h }$

∴ Total time taken is 7d/144 hrs.

$\rule{200}2$

★ Finding average speed :

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }} }$

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( 2d \div \dfrac{7d}{144} \Bigg ) \; kmh^{-1} }$

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( 2d \times \dfrac{144}{7d} \Bigg ) \; kmh^{-1} }$

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( 2 \times \dfrac{144}{7} \Bigg ) \; kmh^{-1} }$

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( \dfrac{288}{7} \Bigg ) \; kmh^{-1} }$

$\longmapsto \bf {Speed_{(avg)} = 41.14 \; kmh^{-1} }$

∴ Average speed is 41.14 km/h.