Question

A car travels first 30 km with a uniform speed of 60 km h-1 and then next 30 km with a uniform speed of 40 km h-1 . Calculate : (a) total time of journey (b) the average speed of car​

Answer 1

Answer :

V1 = 60km/hr D1 = 30 km

T1 = ?

V2 = 40 km /hr D2 = 30 km

T2 = ?

Total Time = T1 + T2

We know that ,

velocity = Distance /Time

Therefore ,

V1 = D1/T1 or T1 = D1 / V1 => T1 = 30 km / 60 km /hr = 1/2 hr

V2 = D2/T2 or T2 = D2/ V2 => T2 = 30 km / 40 km /hr = 3/4 hr

Hence ,

Total Time = T1 + T2 = 1/2 + 3/4 = 5/4 hrs

we know that ,

Average Velocity = Total Distance / total time taken = 30 + 30 / 5/4

= 60/5/4 = 48 km /hr

Hence Average Velocity is 48km/hr and total time of journey = 5/4 hours.

My Short cut Method :-

When a body travels equal distance with different velocities V1 and V2 , then Average Velocity is Calculated as

Average Velocity = 2*V1*V2 / (V1 + V2 )

here , V1 = 60 km/hr and V2 = 40 km/hr

therefore ,

Average Velocity = 2*60*40 / (60+40 )= 4800/100 = 48km/hr

Also we know that ,

Average Velocity = Total Distance / Total Time Taken

48 = 60 / Total Time Taken

or Total Time Taken = 60/48 = 5/4 Hrs .

Hope it helps you buddy...

Good Luck.....