Question 1186764
Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A and travels the same distance in 2 hours less. Find the speed of each.
<pre>Let cyclist A's speed be S
Then cyclist B's speed is: S + 5
We then get the following TIME equation: {{{matrix(1,3, 60/(S + 5) + 2, "=", 60/S)}}}  
{{{matrix(1,3, 30/(S + 5) + 1, "=", 30/S)}}} ------ Factoring out GCF, 2, in the numerator
30S + S(S + 5) = 30(S + 5) ------ Multiplying by LCD, S(S + 5)
{{{matrix(3,3, 30S + S^2 + 5S, "=", 30S + 150, S^2 + 5S + 30S - 30S - 150, "=", 0, S^2 + 5S - 150, "=", 0)}}}
(S - 10)(S + 15) = 0
S - 10 = 0       OR        S + 15 = 0_____S = - 15 (ignore)
{{{highlight_green(matrix(1,8, Cyclist, "A's", "speed:", or, S, "=", 10, "km/h"))}}} 
{{{highlight_green(matrix(1,7, Cyclist, "B's", "speed:", 10 + 5, "=", 15, "km/h"))}}}</pre>