Question 1169435
An express train is 50 kph faster than the freight train. If it takes 2 hour less for the express train to travel 600 km as compare to the freight train, how fast is the express train?
<pre>You don't NEED to find time as the other person suggests!
Let the express train's speed be S
Then the freight train's speed = S - 50
We then get the following TIME equation: {{{matrix(1,3, 600/S + 2, "=", 600/(S - 50))}}}
{{{matrix(1,3, 300/S + 1, "=", 300/(S - 50))}}} ------ Factoring out GCF, 2, in numerator
300(S - 50) + S(S - 50) = 300S ----- Multiplying by LCD, S(S - 50)
{{{matrix(3,3, 300S - "15,000" + S^2 - 50S, "=", 300S, S^2 - 50S - "15,000", "=", 0, "(S - 150)(S + 100)", "=", 0)}}}
S - 150 = 0           OR               S + 100 = 0
Speed of express train, or {{{highlight_green(matrix(1,4, S, "=", 150, "km/h"))}}}            OR              S = - 100 (ignore)