Question

A man covers a distance of 147 km on the motor bike. He starts with speed of x kmph and dou- bles his speed after every 45 minutes. He has to repeat this two times to cover the distance. Find the intial speed of man and also find his average speed. 1) 21 kmph, 65.33 kmph 2) 28 kmph, 65.33 kmph 3) 25 kmph, 70 kmph 4) None of these ​

Answer 1

        $\text{We can arrange the given parameters as following:}$

        $\text{Distance}(s) = 147 \: km$

        $\text{Initial velocity}(u) = x$

        $\text{The question states that his velocity doubles after every 45 min}$

        $\text{Question also states that he has to repe}\text{at it twice to cover the distance}$

        $\text{During First 45 min}$

$\implies \text{Distance covered}(s_1) = \dfrac{45}{60} \times x = 0.75x$

        $\text{During the Second 45 min}$

$\implies \text{Distance covered}(s_2) = 0.75 \times 2x = 1.5x$

$\implies \: s_1 + s_2 = s$

$\implies \: 0.75x + 1.5x = 147$

$\implies \: 2.25x = 147$

$\implies \: \boxed{x = 65.33 \; km/h}$