Question

a cyclist rides his cycle with a speed of 30m/s for the first half and the next half length he covers with speed of 45m/s. find the average speed of the cyclist​

Answer 1

Answer:

The average speed is 36 m/s.

Explanation:

Let the total distance be 'x m'

A cyclist rides his cycle with a speed of 30 m/s for the first half.

Let the time taken be t1.

We know,

Speed = Distance/time taken

30 = x/2/t1

x/2t1 = 30

x/t1 = 60

t1 = x/60

He then covers next half with speed 45 m/s.

Let the time taken here be t2.

Speed = Distance/time taken

45 = x/2/t2

45 = x/2t2

t2 = x/90

The average speed is the ratio of the total distance covered to the total time taken.

Average speed = Total distance/total time taken

$\implies \rm \dfrac{x}{t1 + t2} \\\\ \implies \rm \dfrac{x}{\dfrac{x}{60}+\dfrac{x}{90}} \\\\ \implies \rm \dfrac{1}{\dfrac{1}{60}+\dfrac{1}{90}} \\\\ \implies \rm \dfrac{1}{\dfrac{3+2}{180}} \\\\ \implies \rm \dfrac{1}{\dfrac{5}{180}} \\\\ \implies \rm \dfrac{1}{\dfrac{1}{36}} \\\\ \implies \rm 36 \: m/s$

Therefore, the average speed is 36 m/s.