Question 1164936

x takes 3 hrs more than y to walk 30 km. but if x doubles his pace he is ahead of y by 1 1/2 hours.find their speed of walking
<pre>It may be easier to find the time 1st, but I always like to ZERO IN right away on the answers that're needed.
Let x's and y's speeds be x and y, respectively
We then get the following TIME equation: {{{matrix(2,3, 3, "=", 30/x - 30/y, 1, "=", 10/x - 10/y)}}}
                                         xy = 10y - 10x ------ eq (i)
                            We also get: {{{matrix(3,3, 1&1/2, "=", (- 30)/(2x) + 30/y, 3/2, "=", (- 15)/x + 30/y, 1/2, "=", (- 5)/x + 10/y)}}}
                                         xy = - 10y + 20x ------ eq (ii)
                                         2xy = 10x ------ Adding eqs (i) & (ii)
                                         y's speed, or {{{highlight_green(matrix(1,6, y, "=", 10x/(2x), "=", 5, "km/h"))}}}
                           x(5) = 10(5) - 10x ------ Substituting 5 for y in eq (i)
                           5x = 50 - 10x
                           5x + 10x = 50
                           15x = 50
                           x's speed, or {{{highlight_green(matrix(1,8, x, "=", 50/15, "=", 10/3, or, 3&1/3, "km/h"))}}}