Question

SPEED,DISTANCE AND TIME
Out of a total distance covered of 200 km, first half is covered at the speed of 60 km per hr and the remaining half is covered at 75 km per hr. Find:​​

1. the total time taken to cover the whole journey
2. the average speed for the whole journey

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{Distance}=200\mathrm{km} \\ {\mathrm{S}}_1=60\mathrm{km}/\mathrm{h} \\ {\mathrm{S}}_2=75\mathrm{km}/\mathrm{h} \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \mathrm{Half}\mathrm{is}\mathrm{covered}\mathrm{at}\mathrm{the}\mathrm{speed}{\mathrm{S}}_1\mathrm{and}\mathrm{the}\mathrm{remaining} \\ \mathrm{half}\mathrm{is}\mathrm{covered}\mathrm{at}{\mathrm{S}}_2. \\ \mathrm{a}) \\ \mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}} \\ \Rightarrow \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}} \\ \Rightarrow \mathrm{Time}=\frac{100}{{\mathrm{S}}_1}+\frac{100}{{\mathrm{S}}_2} \\ \Rightarrow \mathrm{Time}=100\left(\frac{1}{60}+\frac{1}{75}\right) \\ \Rightarrow \mathrm{Time}=100\left(\frac{5+4}{300}\right) \\ \Rightarrow \mathrm{Time}=\left(\frac{9}{3}\right) \\ \Rightarrow \mathrm{Time}=3\mathrm{hours} \\ \mathrm{b}) \\ \mathrm{Average}\mathrm{speed}=\frac{\mathrm{Total}\mathrm{Distance}\mathrm{Travelled}}{\mathrm{Total}\mathrm{Time}\mathrm{Taken}} \\ =\frac{200}{3} \\ =66.66\mathrm{km}/\mathrm{h} \end{gathered}$$