Question

A car travels first 30km with a uniform speed of 60 km/h and then next 30 km with a uniform speed of 40 km/h. Calculate :(i) the total time of journey, (ii) the average speed of the 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 .

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