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

Given:

• The speed of car from x to y : 45 km/h
• The speed of car from y to x : 35 km/h

To find:

• The average speed of the car

Solution:

We know that,

• $\sf{Average_{speed}}$ = $\sf{\dfrac{Total\:distance \:travelled}{Total\:time\:taken}}$

Now, for the distance, obviously it will be the same and thus the total distance would be 2d

Now, the speed from x to y be :

Speed = $\sf{\dfrac{Distance}{Time}}$

45 = $\sf{\dfrac{d}{T1}}$

T1 = $\sf{\dfrac{d}{45}}$

Again, the speed from balasore to kolkata be :

Speed = $\sf{\dfrac{Distance}{Time}}$

35 = $\sf{\dfrac{d}{T2}}$

T2 = $\sf{\dfrac{d}{35}}$

Now, just put the values in the formula;

= $\sf{Average_{speed}}$ = $\sf{\dfrac{Total\:distance \:travelled}{Total\:time\:taken}}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{\dfrac{d}{45} +\dfrac{d}{35} }}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{\dfrac{7d + 9d}{315} }}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{\dfrac{16d}{315} }}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{16d} × 315}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2}{16} × 315}$

= $\sf{Average_{speed}}$ = 2 × 19.6

= $\sf{Average_{speed}}$ = 39.2 km/h

Therefore, the average speed of the car is 39.2 km/h.