Question

A car moves four sucessive 6 km stretches at speed 25km/hr 50km/hr 75k/hr 150k/hr its average speed of his journey

Answer 1

$\underline{\mathfrak{\huge{The\:Question:}}}$

A car moves four successive 6 km stretches at speed 25 km/hr , 50 km/hr , 75 km/hr , 150 km/hr. Find it's average speed.

$\underline{\mathfrak{\huge{Your\:Answer:}}}$

Since we have that every speed was there for the same distance travelled, that means, only 6 km, the distance for Every time period will be the same.

The Given speed is :-

$\tt{s_{1} = 25 km/hr}$

Distance will be same :-

$\tt{d_{1} = 6 km}$

The time will be :-

$\tt{t_{1} = \frac{6}{25} hr}$

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The Given speed is :-

$\tt{s_{2} = 50 km/hr}$

The distance will be the same :-

$\tt{d_{2} = 6 km}$

The time will be :-

$\tt{t_{2} = \frac{6}{50} hr}$

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The Given speed is :-

$\tt{s_{3} = 75 km/hr}$

Distance will be the same :-

$\tt{d_{3} = 6 km}$

The time will be:-

$\tt{t_{3} = \frac{6}{75} hr}$

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The Given speed is :-

$\tt{s_{4} = 150 km/hr}$

The distance will be the same :-

$\tt{d_{4} = 6 km}$

The time will be :-

$\tt{t_{4} = \frac{6}{150} hr}$

Now, the average speed will be :-

$\tt{Average\:Speed = \frac{d_{1} + d_{2} + d_{3} + d_{4}}{t_{1} + t_{2} + t_{3} + t_{4}}}$

Find the value of the total time taken :-

● $\tt{t_{1} + t_{2} + t_{3} + t_{4} = \frac{6}{25} + \frac{6}{50} + \frac{6}{75} + \frac{6}{150} }$

● $\tt{t_{1} + t_{2} + t_{3} + t_{4} = \frac{72}{150}}$

● $\tt{t_{1} + t_{2} + t_{3} + t_{4} = 0.48 hrs}$

Put this value in the formula and then solve it :-

=》 $\tt{Average \:Speed = \frac{6 + 6 + 6 + 6 }{0.48}}$

=》 $\tt{Average\:Speed = 50 km/hr}$

That's your answer