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.

Comments

Markov Chaney said…
Maria, I'm not sure how you figured out what the problem was actually asking for. It is so badly written as to appear indecipherable to me. It says,

"8 miles travelled in the second hour. This is 1/7 times more than during the first hour, and 1/4 times more than he travelled at the second hour. Tell me for three hours what is the miles he has covered."

Seems to me that 8 hours travelled in the 2nd hour can't be "1/4 times more than he travelled at the second hour," can it?
Christina in GA said…
I'm not sure how to contact you except through the comments, so here goes. I have to say that I am loving your e-book on multiplication. I have tried to teach my son multiplication for 3 years now and he is FINALLY getting it! I like how you show the different ways to solve the problems. It is finally making sense to him. I'll be purchasing the one on division soon. Thanks for making these e-books, they are wonderful.
Maria Miller said…
Hi Markov,

Well I suspect the person who asked me to solve that was not from U.S. and sort of translated the problem into English the best he could.

I corrected it a little now.

And Christina, thanks for nice comments! I've added a contact me link now in the side bar... the contact form and email are simply on my math site.
Anonymous said…
ur problem rocked ,but it was a bit complicated.

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