Question 1155618
Alexa makes a journey of 430km, traveling 160km by bus and 270km by car. If the car
averages 10km/h faster than the bus and the whole journey takes 5 hours, what is the
speed of the car?
<pre>Once again, this can be done MUCH, MUCH simpler! No need to use the quadratic equation formula!
Let the car's speed be S
Then the bus' speed = S - 10
We then get the following TIME equation: {{{matrix(1,3, 160/(S - 10) + 270/S, "=", 5)}}}
{{{matrix(1,3, 32/(S - 10) + 54/S, "=", 1)}}} ------ Factoring out GCF, 5, in numerator
32S + 54(S - 10) = S(S - 10) -------- Multiplying by LCD, S(S - 10) 
{{{matrix(1,3, 32S + 54S - 540, "=", S^2 - 10S)}}}
{{{matrix(1,3, S^2 - 10S - 86S + 540, "=", 0)}}}
{{{matrix(1,3, S^2 - 96S + 540, "=", 0)}}}
(S - 90)(S - 6) = 0
S, or speed of car = {{{highlight_green(matrix(1,2, 90, "km/h"))}}}           OR            S = 6 (ignore)