Question 1015582
if the speed limit is decreased by 10 km/h on a 100 km stretch of a highway, the trip will take a half hour longer than usual. what is the usual speed limit
<pre>Let usual speed limit be S
Then time taken at usual speed = {{{100/S}}}
Decreasing the speed makes the new speed, S – 10
Time taken at new speed: {{{100/(S - 10)}}}
We then get: {{{100/S = 100/(S - 10) - 1/2}}} 
100(2)(S – 10) = 100(2S) – S(S – 10) ------- Multiplying by LCD, 2S(S – 10) 
{{{200S - 2000 = 200S - S^2 + 10S}}}
{{{S^2 - 200S - 10S + 200S - 2000 = 0}}}
{{{S^2 - 10S - 2000 = 0}}}
(S - 50)(S + 40) = 0
S, or original speed limit = {{{highlight_green(matrix(1,2,50, "km/h"))}}}