Question

a car is going from point x to y with the speed of 45 km per hour and come back from point Y to X with the speed of 35 km per hour find the average speed of car (please give full solution)​

Answer 1

Answer:

39.375 km/h

Explanation:

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

• A car is going from point X to Y with the speed of 45 km/h.
• And, comes back from point Y to X with the speed of 35 km/h.

We are asked to calculate the average speed.

In order to calculate the average speed, firstly we need to find total distance and total time taken.

Let us assume the distance from X to Y as d km.

★ Finding total distance :

$\longmapsto \rm {Distance_{(Total)} = Distance_{(XY)} + Distance_{(YX)} }$

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

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

∴ Total distance covered is 2d km.

$\rule{200}2$

★ Finding total time :

$\longmapsto \rm {Time_{(Total)} = Time_{(XY)} + Time_{(YX)} }$

• Time = Distance ÷ Speed

$\longmapsto \rm {Time_{(Total)} = \dfrac{Distance_{(XY)} }{Speed_{(XY)}} + \dfrac{Distance_{(YX)} }{Speed_{(YX)}} }$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{d }{35} + \dfrac{d }{45} \Bigg ) \; h }$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{9d + 7d}{315} \Bigg ) \; h }$

$\longmapsto \rm {Time_{(Total)} = \dfrac{16d}{315} \; h }$

∴ Total time taken is 16d/315 hours.

★ Finding average speed :

$\longmapsto\bf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }$

$\longmapsto\rm {Speed_{(avg)} = \Bigg ( 2d \div \dfrac{16d}{315} \Bigg ) \; kmh^{-1} }$

$\longmapsto\rm {Speed_{(avg)} = \Bigg ( 2d \times \dfrac{315}{16d} \Bigg ) \; kmh^{-1} }$

$\longmapsto\rm {Speed_{(avg)} = \Bigg ( \dfrac{315}{8} \Bigg ) \; kmh^{-1} }$

$\longmapsto\bf {Speed_{(avg)} = 39.375 \; kmh^{-1} }$

∴ Average speed of the car is 39.375 km/h.