yo4561 Wrote:I have a question on Jeff's Free Manhattan Prep GMAT Hour Weighted Averages video.
I haven't watched it, but I'll give you my thoughts. I can't tell whether your question below is just about why 8:20 - 1:30 = 6:50 or about the setup that got us to that point. If it's just about the subtraction itself, I'd note that the mm:ss format doesn't lend itself to subtraction because base 60 different from our normal base 10 number system, so people (me, ha ha) make mistakes with it. It sounds like you were thinking 8:20 -1:30 = 8.2 - 1.3 = 6.9, but that's not it! 20 seconds is 1/3 of a minute, not 0.2, and 30 seconds is 1/2 of a minute, not 0.3.
Convert the seconds into minutes in decimal form to check the math, and then convert back to mm:ss form:
8:20 - 1:30 = 8.33333 - 1.5 = 6.8333333 = 6 + 5/6 = 6:50
yo4561 Wrote:The question he has is as follows:
"You would like to average a pace of 8 minutes and 20 seconds per mile for your run. So far, you have run 3 miles in 28 minutes. If you run will be a total of 5 miles long, what should your average pace be for the final two miles?"
I was with Jeff all the way until the final part when he set 3/2=x/1 minute and said you are 1 and 1/2 minutes under the 8:20 time. He then subtracted 1 and 1/2 minutes from 8:30 and arrived at 6:50 as the answer. 8:20 -1:30=6:50.
How did he get to 6:50? Why is the answer not 6 minutes and 90 seconds?
There are 3 main ways to do this type of question, I think:
(1) seesaw
(2) wtd avg formula
(3) when you see average, you think sum.
It sounds like Jeff showed the seesaw; if you have questions about that, let me know, but it sounds like you followed Jeff through the ratio reasoning.
Just to show another way, I think (3) is most like our normal "I'm jogging while estimating how fast I need to go" thought process:
-- If you need to average 8 minutes and 20 seconds per mile for your 5-mile run, you have 5*(8.33333) = 41.66666 minutes total to complete the run.
--You have already run for 28 minutes, so you have 41.66666 - 28 = 13.666666 minutes left in order to be on time.
--If you still need to run 2 more miles, the average pace must be 13.66666 min./2 miles = (13:40/2) minutes per mile = 6:50 minutes per mile.
yo4561 Wrote:Another question, is it always recommended to simplify the ratio in the seesaw method for weighted averages, will the seesaw method not work if the ratio is not simplified?
The seesaw will work even if the ratio is not simplified; you just might have an easier time with the math if it's simplified first.
