Answer to Question #322476 in Algebra for Kenth Smith

Question

John can walk 4 miles in the same time it takes Paul to walk 5 miles. John, however, requires 3 mins. Longer time than Paul to walk a mile. Find their rates.

Answer 1

$t_1-time\,\,John\,\,walks\,\,a\,\,mile\\t_2-time\,\,Paul\,\,walks\,\,a\,\,mile\\\left\{ \begin{array}{c} 4t_1=5t_2\\ t_1=t_2+3\\\end{array} \right. \Rightarrow \left\{ \begin{array}{c} 4\left( t_2+3 \right) =5t_2\\ t_1=t_2+3\\\end{array} \right. \Rightarrow \left\{ \begin{array}{c} t_1=15\\ t_2=12\\\end{array} \right. \\Rates:\\v_1=\frac{1}{t_1}=\frac{1}{15}miles/\min \\v_2=\frac{1}{t_2}=\frac{1}{12}miles/\min$