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# Abdul, while driving to school, computes the average speed for his trip to be $20\ km h^{-1}$. On his return trip along the same route, there is less traffic and the average speed is $30\ kmh^{-1}$. What is the average speed for Abdul’s trip?

Given:

Average speed while driving to school, $v_1=20km/h$

Average speed while returning from school, $v_1=20km/h$

To find: Average speed of Abdul\'s trip.

Solution: Suppose, Abdul is driving $x$ kilometre while going to school.

Suppose, the time taken in driving to school be $t_1$, and the time taken in returning from the school be $t_2$.

We know that formula of distance is given as-

$Distance=Speed\times {Time}$

Therefore,

$Time=\frac {Distance}{Speed}$

1. Time taken by Abdul\'s when his average speed is 20km/h.

$t_1=\frac {x}{v_1}$

Putting the given values, we get-

$t_1=\frac {x}{20}$

2. Time taken by Abdul\'s when his average speed is 30km/h.

$t_2=\frac {x}{v_2}$

Putting the given values, we get-

$t_2=\frac {x}{30}$

Now,

We know that, formula for average speed is given as-

$\text {Average Speed}=\frac {\text {Total distance travelled}}{\text {Total times taken}}$

Substituting the required values, we get-

$\text {Average Speed}=\frac {x+x}{t_1+t_2}$

$\text {Average Speed}=\frac {x+x}{\frac {x}{v_1}+\frac {x}{v_2}}$

$(putting\ the\ value\ of\ t_1\ and\ t_2)$

$\text {Average Speed}=\frac {2x}{\frac {x}{20}+\frac {x}{30}}$

$\text {Average Speed}=\frac {2x}{\frac {3x+2x}{60}}$

$\text {Average Speed}=\frac {2x}{\frac {5x}{60}}$

$\text {Average Speed}=\frac {2x\times {60}}{5x}$

$\text {Average Speed}=\frac {120x}{5x}$

$\text {Average Speed}=24km/h$

Thus, the average speed of Abdul\'s trip is 24 km/h.

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