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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.