Hey, this is Presh Talwalkar.
If Sue runs around the track twice,
and John runs around the track 4 times more than Sue,
How many times does John run around the track?
This problem caused some confusion after it was assigned to 3rd graders.
The teacher was marking one number as the correct answer
and a parent believed another number was the correct answer.
The problem was then posted online,
and many people believe the correct answer was a third number!
So what's the correct answer?
In this video, I'm going to present 3 different ways to interpret this problem,
and suggest what is the correct answer according to modern usage.
The heart of the confusion is the phrase "four times more than".
Typically, this phrase refers to multiplication.
"times more" means that John runs around the track
four times more than the number of times that Sue runs.
So we take 4 times 2 to get to the answer of 8.
Other people had a different interpretation of this problem.
They read this as saying "John runs around four times more" as in addition.
So if Sue runs around the track 2 times,
John runs around 4 more laps than Sue.
This is 4 more times.
So the number of times that John would run would be 4 plus 2, which equals 6.
The problem with this interpretation is we usually write "More times"
when we're referring to addition.
And when we have the phrase "times more" we're usually referring to multiplication.
There's a third way to read this problem which would be literally correct
according to these words on a strict grammatical basis.
The literal version of this problem is often used in terms of percentages.
"Times more than" would mean you should add that number of times to the base.
So think about this in terms of percentages.
100% more than 2 is a total of 4.
200% more than 2 is a total of 6.
300% more than 2 is a total of 8,
and 400% more than 2 is a total of 10.
So 400% more is the same thing as 4 times.
So having 4 times more than Sue,
would mean 4 times 2 plus 2, which would equal 10 times.
So this is an interpretation that is literally correct,
according to the way the sentence is written.
However, in common usage,
"4 times more" is the phrase that is commonly used in multiplication,
to mean 4 times larger.
You'll see this in newspaper every single day.
A more literal and correct way to refer to multiplication,
would be writing "4 times as much as".
And you'll see that many writers use the phrase "times as much as"
to mean multiplication. It's a very strict way of writing it.
So I would caution you against using this literal interpretation unless you see percentages.
So in conclusion, of these three interpretations,
I would say the correct answer is 8.
because "times more" usually refers to multiplication,
and even "times more than" refers to multiplication.
So if John runs 4 times more than Sue,
the correct answer to this problem would be he would run 4 times 2 which is 8 times around the track.
What do you think the correct answer should be?
Let us know in the comments.
Thanks for watching this video, please subscribe to my channel,
I make videos on math and game theory,
You can catch me on my blog "Mind Your Decisions"
which you can follow on Facebook, Google+ and Patreon,
You can catch me on social media @preshtalwalkar
And if you like this video, please check out my books, there are links in the video description.