Question

A body covers a total distance of $S$. Initial $\frac{S}{3}$ is covered with speed 10 km/hr and next $\frac{2S}{3}$ is with $v$. If average speed is 8 km/hr, find $v$.

• A. 6 km/hr
• B. 5.2 km/hr
• C. 7.2 km/hr
• D. 4.2 km/hr

Answer 1

The correct option is C 7.2 km/hr

$V_{\text{avg}}=\frac{S}{t}=\frac{S}{\frac{\frac{S}{3}}{10}+\frac{\frac{2S}{3}}{v}}=\frac{1}{\frac{1}{30}+\frac{2}{3v}}$

$\frac{1}{30}+\frac{2}{3v}=\frac{1}{8}$

$\frac{2}{3v}=\frac{1}{8}-\frac{1}{30}=\frac{22}{240}$

$v=\frac{2}{3}\times \frac{240}{22}=\frac{160}{22}=\frac{80}{11}\simeq 7.2\text{km/hr}$