Question 1162900
Edward takes 15 minutes longer than Kate does to make the 112-mile drive between two cities. Kate drives 8 miles an hour faster. How fast do Edward and Kate drive?
<pre>Let Edward's speed be S
Then Kate's is: S + 8
We then get the following TIME equation: {{{matrix(1,7, 112/S, "=", 112/(S + 8) + 15/60, "=====>", 112/S, "=", 112/(S + 8) + 1/4)}}}
112(4)(S + 8) = 112(4)(S) + S(S + 8) ------ Multiplying by LCD, 4S(S + 8)
{{{matrix(1,3, 112(4S) + 112(4)(8), "=", 112(4S) + S^2 + 8S)}}} 
{{{matrix(1,3, 0, "=", 112(4S) + S^2 + 8S - 112(4S) - 112(4)(8))}}} 
{{{matrix(1,3, 0, "=", S^2 + 8S - 112(32))}}} 
{{{matrix(1,3, 0, "=", S^2 + 8S - "3,584"))}}} 
(S - 56)(S + 64) = 0
Edward's speed or {{{highlight_green(matrix(1,4, S, "=", 56, mph))}}}        OR            S = - 64 (ignore)
Can you now find Kate's speed?