Problem on proportional reasoning

I'm just going to solve here on the blog another math problem that was sent in to me... Hopefully it helps some of you to learn how to solve problems (you can let me know!)

A man travelled 8 miles in the second hour. This is 1/7 times more than during the first hour, and 1/4 times more than he travelled during the third hour. What is the total miles he covered in three hours?


In this problem, it is easy to get "deceived" and think that you'd just go 1/7 × 8 miles or something like that.

But think first; did the man cover MORE miles during the first hour than during the second hour?

Yes; it says plainly that the 8 miles was 1/7 times MORE than what he covered during the first hour.

Is that 8 miles a LOT more, or a LITTLE BIT more than what he traveled during the first hour?

It's 1/7 times more, so it's a little bit more.

So simply mark as x the miles covered during the first hour. Then,

8 miles = 1 1/7 x

It's not 1/7 x, but 1 1/7 x, or 8/7x. If you put down 1/7 x, you're finding the seventh part, but it was seventh part MORE.

So 8 miles = 8/7x

Multiply both sides by 7, and divide by 8:

x = 7 miles.

Then the last hour. Again the miles traveled during the second hour are more than the miles traveled during the third hour. If miles traveled during the third hour are y, then we get,

8 miles = 1 1/4 y

8 miles = 5/4 y

y = 32/5 miles, or 6 2/5 miles.

Total he covered 7 mi + 8 mi + 6 2/5 mi = 21 2/5 miles or 21.4 miles.
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