Question 270675

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

OK.

We know that average speed or rate: r(av)=(total distance)/(total time)
Let d=total distance from station A to Station B

Then total time is the sum of the times listed below:
time to travel 1/6 distance =(d/6)/90=d/540
time to travel 2/3 or 4/6 the distance=(4d/6)/120=d/180
time to travel the remaining 9 km=9/90=1/10

Now lets look at what we have, first:
1/6 of the distance plus 2/3 of the distance = 5/6 of the distance leaving 1/6 of the distance remaining which we are told is 9 km
So, if (1/6)d=9, then the total distance (d)=54 km

Therefore total time would be:
 54/540 + 54/180 + 1/10 simplify
1/10 + 27/90 +1/10  multiply each term by 90/90
9/90 +27/90 +9/90=45/90=1/2 hr

So, Average Speed (rav)=54/(1/2)=108 km/hr

Hope this helps---ptaylor