Math Is Fun Forum

fleetfilly

Member

Registered: 2007-02-20

Posts: 3

HELP! Finding the slope in a word problem.

I need to find the slope in the following problem.

Driving down a mountain, Tom descends 1800 ft in elevation by the time he is 3.25mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundred.

Can I find the slope with only this information?   When I try to use the given info, I keep coming up with an undefined slope and that just doesn't sound right.  Can anyone please help??

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: HELP! Finding the slope in a word problem.

You can find the slope fairly easily, yes. It's just the change in height divided by horizontal distance travelled.

In this case, that would be -1800/(3.25*3*1760). (3.25 miles converted into feet so that the measurements match)

However, at this point the question does something a bit weird. The horizontal distance is quite a bit bigger than the vertical distance, which means that the slope will be close to 0. Between -1 and 1, anyway. So by asking you to round to the nearest hundred, you have to say that the slope is 0.

But then that would mean that the slope is completely flat, and Tom probably wouldn't be very happy if you told him that because he's just worn out all of his brakes by driving down that steep hill. So it's a bit of a weird question.

---

Why did the vector cross the road?
It wanted to be normal.

fleetfilly

Member

Registered: 2007-02-20

Posts: 3

Re: HELP! Finding the slope in a word problem.

Thanks! I was doing the problem correctly, but .11 didn't seem like much of a slope to me either!

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: HELP! Finding the slope in a word problem.

The slope is 0.104895.   I noticed you rounded your answer to the nearest hundredth.   Is that was the instructions said (round to the nearest hundredth instead of to the nearest hundred)?   If so, you should round to 0.10.

And I would leave the answer as a positive number.   You're going downhill (rise) which is a expressed as a negative number but there is no way to determine whether the horizontal movement (run) is positive or negative.   Besides, the question asks for the "slope of the descent" which already implies the direction.

fredekr

Member

Registered: 2007-02-20

Posts: 5

Re: HELP! Finding the slope in a word problem.

Since the problem is written

the the nearest hundred

we'd have to say that mathsyperson is technically right by saying zero.

But, being that we're human beings, we can detect that probably the problem probably meant to say

to the nearest hundredth

so pi man should have the intended answer.

best,
Kevin