Question

A journalist drove his car with speed 60 km/hr to travel from Kolkata to Balasore to cover the cyclone Josh. But he failed to reach the spot and anticipating the danger ahead he immediately rushed back to Kolkata driving his car with speed 90 km/hr. Find the average speed of the whole journey. If answered right then I will give u marks ​

Answer 1

Given:

• The speed of car to balasore : 60 km/h
• The speed of car to kolkata : 90 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 kolkata to balasore be :

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

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

T1 = $\sf{\dfrac{d}{60}}$

Again, the speed from balasore to kolkata be :

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

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

T2 = $\sf{\dfrac{d}{90}}$

Now, just put the values in the formula;

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

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{\dfrac{d}{60} +\dfrac{d}{90} }}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{\dfrac{3d + 2d}{180} }}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{\dfrac{5d}{180} }}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2d}{5d} × 180}$

= $\sf{Average_{speed}}$ = $\sf{\dfrac{2}{5} × 180}$

= $\sf{Average_{speed}}$ = 2 × 36

= $\sf{Average_{speed}}$ = 72 km/h

Therefore, the average speed of the car is 72 km/h.

Answer 2

We know,

Average speed = $\frac{Total Distance}{Total time}$

Distance travelled from kolkata to Balasore or returning back from Balasore to Kolkate is ofcourse same ( Lets say x)

Total distance travelled by journalist in the entire jouney is 2x.

But it is obvious that the time taken to reach balasore and returing back will take different time( Lets say t1 and t2)

∴t1 =  x/60

∴t2= x/90

Now using the average speed formula, we get

⇒ Average speed = $\frac{x+x}{x/60+x/90}$

Solving which we get, average speed as 72 km / hr.

TSR