Question 1054463

A teacher drove 280 miles to attend a conference and arrived 1 hour late. The teacher calculated that had she increased her average speed by 5 miles per hour, she would have arrived on time. What was her average speed?
<pre>Let average speed to cover distance be S
Then hypothetical speed = S + 5
We then get the following TIME equation: {{{280/S = 280/(S + 5) + 1}}}
280(S + 5) = 280S + S(S + 5) ------- Multiplying by LCD, S(S + 5)
{{{280S + "1,400" = 280S + S^2 + 5S}}}
{{{S^2 + 280S + 5S - 280S - "1,400" = 0}}}
{{{S^2 + 5S - "1,400" = 0}}}
(S – 35)(S + 40) = 0
S, or {{{highlight_green(matrix(1,5, average, speed, "=", 35, mph))}}}    	OR	S = - 40 (ignore)