Question 83385
t = times for each, which are equal
t = distance/rate
Let m = motorcycles rate
{{{t = 40/m}}}
{{{t = 15/(m-20)}}}
{{{40/m = 15/(m-20)}}}
multiply both sides by {{{m*(m-20)}}}
{{{40*(m-20) = 15m}}}
{{{40m -800 = 15m}}}
subtract 15m from both sides
{{{25m - 800 = 0}}}
{{{25m = 800}}}
{{{m = 32}}} mph motorcycle speed
{{{m-20 = 12}}} mph bikes speed
check
{{{40/m = 15/(m-20)}}}
{{{40/32 = 15/12}}}
{{{5/4 = 5/4}}}
OK