Question 982361

On a journey of 100km, Jim travels at a certain speed for the first 60km, and then increases his speed by 15km/h for the remainder. If the whole journey takes 2 hours, find his two speeds.
I'm in year 10, and this is an A-standard question which neither of my parents nor I could solve.
<pre>Let speed on 1st part of trip be S
Then time taken to travel 60 km = {{{60/S}}}
On the 2nd part of trip, a 15 km/h increase in speed results in a speed of S + 15
Then time taken to travel the remaining 40 (100 - 60) km is: {{{40/(S + 15)}}}
Since total time was 2 hours, then we can say that:
{{{60/S + 40/(S + 15) = 2}}}
60(S + 15) + 40S = 2(S)(S + 15) ------- Multiplying by LCD, S(S + 15)
{{{60S + 900 + 40S = 2S^2 + 30S}}}
{{{100S + 900 = 2S^2 + 30S}}}
{{{2S^2 + 30S - 100S - 900 = 0}}}
{{{2S^2 - 70S - 900 = 0}}}
{{{2(S^2 - 35S - 450) = 2(0)}}}
{{{S^2 - 35S - 450 = 0}}}
(S - 45)(S + 10) = 0
S, or speed on 1st part of trip = {{{highlight_green(45)}}} km/h			OR			S = - 10 (ignore)
Speed on 2nd part of trip: 45 + 15, or {{{highlight_green(60)}}} km/h