Question 1012510

A train averaged 120km/h for the first 80% of a trip and 90km/h for the whole trip. Find it's average speed for the last 20% of the trip.
<pre>Let distance traveled on entire journey be D
Then distance traveled on 1<sup>st</sup> 80% = .8D
Time taken to travel 1<sup>st</sup> 80% of journey = {{{.8D/120}}}
Let speed during last 20% of trip be S
Since distance traveled on last 20% = .2D, then
Time taken to travel last 20% of journey = {{{.2D/S}}}

Total distance: D 
Total time: {{{.8D/120 + .2D/S}}}
Average speed = Total distance, divided by total time, OR
{{{90 = D/(.8D/120 + .2D/S)}}}
{{{90(.8D/120 + .2D/S) = D}}} ----- Cross-multiplying
{{{90 * (.8D/120) + 90(.2D/S) = D}}}
{{{.6D + 18D/S = D}}}
.6DS + 18D = DS ------- Multiplying by LCD, S
D(.6S + 18) = D(S) ---- Factoring out GCF, D
.6S + 18 = S
18 = S - .6S
18 = .4S
S, or speed on 2<sup>nd</sup> leg of journey = {{{18/.4}}}, or {{{highlight_green(45)}}} km/h