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hoangcfa
11-15-2004, 04:51 AM
Comparison question:

A train makes a 50-mile trip at an average speed of 45 miles/h. The train travels at an average speed of 40m/h for the first 30 miles of the trip.

A. The train's average speed for the last 20 miles of trip
B. 45m/h.

Key: A

Please help me with explanation.
Many thanks.
HCFA

lmtuan
11-15-2004, 05:55 AM
Let X be the train's average speed for the last 20 miles of trip. We have:
50/{ 30/40 + 20/X} = 45
50/45 = 30/40 + 20/X
50/45 - 30/40 = 20/X
(400 - 270)/360 = 20/X
130/360 = 20/X
X = 360*20/130
X = 720/13 > 45
Thus, answer: A

hoangcfa
11-15-2004, 10:14 PM
Thank so much, Tuan.

swethav12
11-19-2004, 01:31 AM
total trip =50
avg speed for total trip =45
first 30 miles was at the speed of 40miles/hr so let rest of the miles be X

(X+40)/2 =45miles/hr
=> X=50 miles/hr
so answer is A

lorcar
11-22-2004, 06:59 PM
i would not do all these calculations

The TOTAL average is 45.
We have the first average, 40, and we know that the speed in the last 20 minutes should be so high that the TOTAL become 45.
THEN the average in the last 20 is definitively higher than 45

krakow
11-22-2004, 07:45 PM
i would not do all these calculations

The TOTAL average is 45.
We have the first average, 40, and we know that the speed in the last 20 minutes should be so high that the TOTAL become 45.
THEN the average in the last 20 is definitively higher than 45
excellent shortcut! [clap]

777
11-22-2004, 08:22 PM
I think that's what I would have done. Is it good or bad to not even do the calculations if you are stressed for time? What about the possibility of mistake?

bigduke
11-22-2004, 08:39 PM
well there's this thing I call interpretational math, this is just a classic example of that. usually the answer is manifest by the question itself, just look at the keys. :)
No chance of mistake.

777
11-22-2004, 09:06 PM
"Keys"? You mean clues in the questions? Yeah, this educated guessing comes in quite useful during QC but not nearly as applicable in PS. I often get paranoid sometimes though because I often second-guess myself on whether I've missed out on something by rushing through so fast, so I don't know if this technique is quite that sound as doing the full calculation. Also, I think it works on the easy questions but the questions that I'm expecting on the actual exam, harder ones, I don't know I'll be able to do it.

lorcar
11-22-2004, 11:24 PM
excellent shortcut! [clap]
thanks!
it's nice to save one minute sometime, when you know that for most of the other single questions you'll need 15 minutes.....:yuck: