Question

3. A ear is going from point X to Y with the speed 45 km/hour and come back from point Y to X with thespeed 35 km/hour. Find the average speed of car.​

Answer 1

Answer:

39.375 km/h

Explanation:

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

• A car is going from point X to Y with the speed 45 km/hour and come back from point Y to X with the speed 35 km/hour.

We are asked to calculate the average speed of car.

Average speed of the car is the total distance travelled divided by total time.

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

Calculating total distance :

• Let us say that the distance from X to Y is d km.

As, the body goes from point X to Y and then comes back from Y to X. So,

⇒ Total distance travelled = XY + YX

⇒ Total distance travelled = (d + d) km

⇒ Total distance travelled = 2d km

∴ Total distance travelled is 2d km.

Calculating total time :

⇒ Total time taken = t₁ + t₂

• t₁ is time taken to cover the distance from X to Y.
• t₂ is time taken to cover the distance from Y to X.

$\longmapsto \rm {Time_{(Total)} = Time_{(X \; to \; Y)} + Time_{( Y \; to \; X)} }$

• Time = Distance/Speed

$\longmapsto \rm {Time_{(Total)} = \dfrac{Distance_{( X \; to \; Y)} }{Speed_{( X \; to \; Y)}} + \dfrac{Distance_{( Y \; to \; X)}}{Speed_{( Y \; to \; X)}} }$

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

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

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

∴ Total time taken is 16d/315 hours.

Calculating 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 is 39.375 km/h.