Question

riya travels 300 km to her home partly by train and by bus. she travels 60 km by train in 4 hours and remaining by bus. if she travels 100 km by train and the remaining by bus, she takes 10 min more. find the speed of train and bus separately

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{train}\mathrm{be}\mathrm{x}\mathrm{km}/\mathrm{hr}\mathrm{and}\mathrm{speed}\mathrm{of}\mathrm{bus}\mathrm{be}\mathrm{y}\mathrm{km}/\mathrm{hr}. \\ \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}} \\ \mathrm{As}\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{she}\mathrm{travels}60\mathrm{km}\mathrm{by}\mathrm{train}\mathrm{in}4\mathrm{hours}. \\ \mathrm{So}, \\ 4=\frac{60}{\mathrm{x}} \\ \mathrm{x}=15\mathrm{km}/\mathrm{hr} \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \frac{60}{\mathrm{x}}+\frac{240}{\mathrm{y}}+\frac{10}{60}=\frac{100}{\mathrm{x}}+\frac{200}{\mathrm{y}} \\ \frac{60}{15}+\frac{240}{\mathrm{y}}+\frac{10}{60}=\frac{100}{15}+\frac{200}{\mathrm{y}} \\ \frac{240}{\mathrm{y}}-\frac{200}{\mathrm{y}}=\frac{100}{15}-\frac{60}{15}-\frac{10}{60} \\ \frac{40}{\mathrm{y}}=\frac{400-240-10}{60} \\ \frac{40}{\mathrm{y}}=\frac{150}{60} \\ \mathrm{y}=16\mathrm{km}/\mathrm{hr}. \\ \mathrm{Speed}\mathrm{of}\mathrm{train}\mathrm{is}15\mathrm{km}/\mathrm{hr}\mathrm{and}\mathrm{speed}\mathrm{of}\mathrm{bus}\mathrm{is}16\mathrm{km}/\mathrm{hr}. \end{gathered}$$