bpgen wrote:A riverboat leaves Mildura and travels upstream to Renmark at an average speed of 6 miles/hr. It returns by the same route at an average speed of 9 miles/hr. What is the average speed of the round trip, in miles/hr?
A- 7.0
B- 7.2
C- 7.8
D- 7.8
E- 8.2
There are a number of ways we could approach this question, including solving equations, using weighted averages and a matrix. The third option works for all multiple part distance/rate/time questions and will almost certainly be applicable on test day.
Across the top of the matrix we have the applicable formula: distance = rate * time.
Down the side of the matrix we have the parts of the trip and the entire trip: upstream, downstream, total.
To start, it looks like this:
..............Distance....=......Rate............*..............Time
Upstm........D......................6.................................t(up)
Dnstm........D......................9.................................t(dn)
Total.........2D.....................r...............................t(up) + t(dn)
Now, we could solve as is, or we could make our lives easier by picking a distance - no matter what number we choose, we'll always get the same average rate. Since we're going to be dividing distance by rate, we want a distance divisible by both 6 and 9 - let's choose 18.
So, back to our chart:
..............Distance....=......Rate............*..............Time
Upstm........18......................6.................................t(up)
Dnstm........18......................9.................................t(dn)
Total...........36.....................r...............................t(up) + t(dn)
Now we can solve for t(up) and t(dn):
..............Distance....=......Rate............*..............Time
Upstm........18......................6.................................3
Dnstm........18......................9.................................2
Total...........36......................r.................................5
Finally, we solve the total equation on the bottom line:
36 = r*5
36/5 = r
7.2 = r
One of the primary advantages of the matrix is that it allows you to see what information you have and what pieces are missing, so you can plan your attack to find whatever that particular question is asking about.
