kaplan question

Hi, here's how I solved the problem.

1) Make an assumption about how long the trip is between Milbura and Renmark. I chose 18 miles because it's evenly divisible by 6 and 9.

2) Determine the number of hours it takes to get from Milbura to Renmark at 6mph and then vice-versa at 9mph. Here's the equation:

(18miles/6mph)+(18miles/9mph) = 3+2 = 5 hours

3) Now determine the TOTAL miles per TOTAL hours: 18+18 miles=36 miles/5 hours = 7.2 mph.

Your brain immediately wants to say "well, duh, it's 7.5mph!" but the boat is spending more time on the river going 6mph then 9mph, thus the average is shifted a little more towards 6mph.

Is the answer B (7.2)?

Total distance/total time: (d)/(T1+T2)

Let X equal the distance between Milbura and Renmark. Boat travels this distance twice, hence X+X or d.

Let T equal the time it takes to travel between each town. Since rate x time = distance, we have 6 x T1=X and 9 x T2=X.

So plugging in, we have (X+X)/((X/6)+(X/9))=
=2X/(10X/36)
=72X/10X
=72/10
=7.2

A riverboart leaves Milbura and travels upstream to Renmark at an average speed of 6 miles per hour. it returns by the same route at an average speed of 9 miles per hour. What is its average speed for the round-trip, in miles per hour?

A. 7.0
B 7.2
C 7.5
D 7.8
E 8.2

Upstream Speed = (Speed of Boat - Speed of Stream)
Downstream Speed = (Speed of Boat + Speed of Stream)
Let the riverboat travel 360 km one way
Total distance traveled = 360*2 = 720
Time taken Upstream = 360/6 = 60 hrs
Time taken Downstream = 360/9 = 40 hrs
Average Speed = Total Dis/Total Time = 720/100 = 7.2

Thanks for both - Yes the answer is B).

When distance travelled is the same both ways (like in the prob above)then the shortcut to find average speed is

Average speed = 2 * speed1 * speed2 / speed1 + speed2

2*9*6/9+6 = 108/15 = 7.2