1/2 part of a certain journey is covered at the speed of 10 km/hr, 1/4 part of the journey is covered at the speed of 5 km/hr and the remaining part covered at the speed of 5 km/hr. What will be the average speed for the whole journey? 

1/2 part of a certain journey is covered at the speed of 10 km/hr, 1/4 part of the journey is covered at the speed of 5 km/hr and the remaining part covered at the speed of 5 km/hr. What will be the average speed for the whole journey?  Correct Answer 6.67

Given: 

1/2 part of journey is covered at the speed of = 10 km/h

1/4 part of journey is covered at the speed of = 5 km/h

And the remaining part of journey at the speed of = 5 km/h

Formula used:

Speed = Distance/Time

Calculation: 

Let the total distance be = S km

According to question,

First part = S/2, Second part = S/4 and the remaining part = S – (S/2 + S/4) = S/4

time taken to cover 1/2 part of distance = (S/2)/10

⇒ S/20

Time taken to cover ¼ part of distance =  (S/4)/5

⇒ S/20

And the remaining part of distance in time in = (S/4)/5

So, the total time = S/20 + S/20 + S/20 = 3S/20

So, the Average speed = total distance/ total time

Average speed = S/(3S/20)

⇒ Average speed = 20/3

∴ The average speed of the whole journey will be 6.67 km/hr

Short trick:

1/2, 1/4 take in lcm in denominator = 80 km (let total distance)

1/2 × 80 = 40, 1/4× 80 = 20

Then remaining part of distance is = 80 – (40 + 20) = 20 km

So, using the formula = speed = distance/time

⇒ 40/10 + 20/5 + 20/5 = 4 + 4 + 4 = 12 (total time)

Average speed = 80/12

∴ Average speed =      6.67