Question

A man completed a certain journey by a car. He covered 1/3^rd of the journey at 40 km/h, 1/6^th of journey at 60 km/h and the remaining journey at x km/h. If his average speed for the whole journey is 10 m/sec. Find X in km/h
1. 30
2. 25
3. 20
4. 40

Answer 1

Correct Answer - Option 1 : 30

Given:

Average speed of the whole journey = 10 m/s = 10 × 18/5 = 36 km/h

Speed of man for 1/3^rd of his journey = 40 km/h

Speed of man for 1/6^th of his journey = 60 km/h

Remaining journey = 1 – (1/3 + 1/6) = 1/2 of his journey = x km/h

Formula used:

Time = Distance/Speed

Average speed = Total distance travelled/Total time taken

Calculation:

Let, Total distance = D km

1/3^rd of journey = D/3 km,

Time taken at 40 km/h = (D/3)/40 = (D/120) h

1/6^th of journey = D/6 km,

Time taken at 60 km/h = (D/360) h

1/2^nd of journey = D/2 km,

Time taken at X km/h = (D/2x) h

Now, Average speed = D/(D/120 + D/360 + D/2x) = 36

⇒ 1/(1/120 + 1/360 + 1/2x) = 36

⇒ 360x/(3x + x + 180) = 36

⇒ 10x = 4x + 180

⇒ 6x = 180

⇒ x = 180/6 = 30 km/h

∴ Remaining 1/2^nd of the journey he travelled at 10 km/h