Question

A man travells80 miles in 6 hours by car. He travelled the first part with a speed of 10 miles/hour ,and last part he travelled 18 miles /hour . Find the part of trip covered at 18 miles /hour

Answer 1

$$\begin{gathered} \mathrm{He}\mathrm{travells}80-\mathrm{miles}\mathrm{in}6\mathrm{hour} \\ \mathrm{so}\mathrm{let}\mathrm{first}\mathrm{part}\mathrm{is}\mathrm{x}\mathrm{and}\mathrm{second}\mathrm{part}\mathrm{is}\mathrm{y}\mathrm{so} \\ \mathrm{x}+\mathrm{y}=80....\left(1\right) \\ \mathrm{also}\mathrm{t}={\mathrm{t}}_1+{\mathrm{t}}_2 \\ 6=\frac{\mathrm{x}}{10}+\frac{\mathrm{y}}{18} \\ \frac{\mathrm{x}}{10}+\frac{80-\mathrm{x}}{18}=6 \\ \frac{9\mathrm{x}+400-5\mathrm{x}}{90}=6 \\ 4\mathrm{x}+400=540 \\ 4\mathrm{x}=140 \\ \mathrm{x}=35\mathrm{so}\mathrm{y}=80-\mathrm{x}=45\mathrm{miles}\mathrm{so}\mathrm{answer}=45\mathrm{miles} \end{gathered}$$