Question

A car travels from A to B at a speed of 30 km/hr and returns at a speed of 40 km/hr. Then the average speed of the car for the whole journey is:
1. 34.29 km/hr
2. 38.6 km/hr
3. 42.4 km.hr
4. 40 km/hr

Answer 1

Correct Answer - Option 1 : 34.29 km/hr

CONCEPT:

Average speed:

• The total path length traveled divided by the total time interval during which the motion has taken place is called the average speed of the particle.
• Mathematically it is written as,

\(Average\;speed\;\left( {\bar v} \right) = \frac{{total\;path\;length\;\left( S \right)}}{{total\;time\;taken\;\left( t \right)}}\)

CALCULATION:

Given s₁ = 30 km/hr and s₂ = 40 km/hr

Let the distance between A and B be x.

So the time required to travel from A to B is given as,

\(⇒ t_{1}=\frac{x}{s_{1}}\)

\(⇒ t_{1}=\frac{x}{30}\) hr     -----(1)

So the time required to travel from B to A is given as,

\(⇒ t_{2}=\frac{x}{s_{2}}\)

\(⇒ t_{2}=\frac{x}{40}\) hr     -----(2)

The total distance covered is given as,

⇒ x' = x + x

⇒ x' = 2x     -----(3)

• The average speed is given as,

\(⇒ s = \frac{total \,distance}{total\, time}\)

\(⇒ s = \frac{2x}{t_{1}+t_{2}}\)

\(⇒ s = \frac{2x}{\frac{x}{30}+\frac{x}{40}}\)

⇒ s = 34.29 km/hr

• Hence, option 1 is correct.