In a journey of $100 k m$ , a car travels first $25 k m$ with a constant velocity of $50 k m h^{- 1}$ , then it covers next $50 k m$ in $15 m i n$ and remaining $25 k m$ it travels with a speed of $100 k m h^{- 1}$ . Determine the average speed of the car's journey.

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Solution

Step 1: Given Data
Total Distance traveled by car, $s = 100 k m$
Let $s_{1}, s_{2}$ and $s_{3}$ be the distance traveled by car with three different velocities respectively then,
$s_{1} = 25 k m$
$s_{2} = 50 k m$
$s_{3} = 25 k m$
The velocity of the car for $s_{1}, v_{1} = 50 k m h^{- 1}$
The velocity of the car for $s_{3}, v_{3} = 100 k m h^{- 1}$
Time is taken to cover the distance $s_{2}, t_{2} = 15 m i n = 0.25 h$
Step 2: Find the time taken by car in traveling $s_{1}$ and $s_{2}$ the distance.
The time is taken for traveling the distance $s_{1}$
$T i m e = \frac{D i s \tan c e c o v e r e d}{V e l o c i t y}$
$t_{1} = \frac{s_{1}}{v_{1}} = \frac{25}{50} = 0.5 h$
Similarly, the time taken for traveling the distance $s_{3}$
$t_{3} = \frac{s_{3}}{v_{3}} = \frac{25}{100} = 0.25 h$
Step 3: Find the average speed of the car
Average speed is the total distance traveled divided by the total time taken.
$A v e r a g e S p e e d = \frac{T o t a l d i s \tan c e}{T o t a l t i m e} = \frac{s}{t_{1} + t_{2} + t_{3}} = \frac{100}{0.5 + 0.25 + 0.25} = \frac{100}{1} = 100 k m h^{- 1}$
Final Answer:
The average speed of the car's journey is $100 k m h^{- 1}$ .

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