Question

A car travels the first half of a distance between two places a speed of 30km /hr and the second half of the distance a50km/hr. The average speed of the car for the whole journey is

Answer 1

A car travels the first half of a distance between two places a speed of 3 0km/hr and the second half with a speed of 50km/hr.

We have to find the average speed of the car during the whole journey.

Now,

Average speed is defined as the ratio of total distance covered with respect to total time taken.

As the distance covered by the car is same i.e. x km. In first half distance covered is x km and in second half distance covered is x km. So, the total distance covered by the car is 2x km.

Also,

Time = Distance/Speed

t1 = x/30 hr and t2 = x/50 hr

Total time taken = t1 + t2

= x/30 + x/50

= x/5(4/15)

= 4x/75

Average speed = 2x/(4x/75)

= (2*75)/4

= 37.5

Therefore, the average speed of the car for the whole journey is 37.5 km/hr.

Shortcut Method

Average speed = (2 × S1 × S2)/(S1 + S2)

= (2 × 30 × 50)/(30 + 50)

= 3000/80

= 37.5 km/hr

Answer 2

Given:

• Car travells first half with speed = 30km/h
• And second half with speed = 50km/h

To find:

• Average speed

Solution:

Let the half distance be x

Total distance = 1/2 of distance + other 1/2

Total distance = x + x

Total distance = 2x

Now, finding total time

Time = distance/speed

Total time = t1 + t2

t1 = x/30

t2 = x/50

Total time = x/30 + x/50

Total distance = 4x/75

Now,

Average speed = Total distance/total time

Avg speed = 2x/4x/75

Avg speed = 150x/4x

Avg speed = 150/4

Avg speed = 37.5 km/h

Hence , average speed = 37.5 km/h