Question 1122925

 A motorist travels 60 km at x km/hr and 180 km at y km/hr and takes 10 hours altogether for the journey. If the speeds are interchanged, the journey takes 8hr 40mins. Find x and y  
<pre>{{{matrix(1,3, 60/x + 180/y, "=", 10)}}}
60y + 180x = 10xy ------ Multiplying by LCD, xy ------ eq (i)

{{{matrix(1,7, 180/x + 60/y, "=", 8&2/3,"_______", 180/x + 60/y, "=", 26/3)}}}
540y + 180x = 26xy ----- Multiplying by LCD, 3xy ------- eq (ii)
480y = 16xy ------------ Subtracting eq (i) from eq (ii)
{{{highlight_green(matrix(1,6, x, "=", (480y)/(16y), "=", 30, "km/h"))}}}

{{{matrix(1,3, 60/30 + 180/y, "=", 10)}}} ------ Substituting 30 for x in eq (i)
{{{matrix(1,3, 2 + 180/y, "=", 10)}}} 
2y + 180 = 10y
180 = 10y - 2y
180 = 8y
{{{highlight_green(matrix(1,6, y, "=", 180/8, "=", 22.5, "km/h"))}}}