Question

Help with application problem

Answer 1

Your college quadrangle is 85 meters long and 66 meters wide. When you are late for class, you can walk at 7 miles per hour. You are at one corner of the quad and your class is directly opposite corner. How much time can you save by cutting across rather than going around the edge.

Answer 2

So i sketched it out

Answer 3

Pythagorean Theorem

Answer 4

85^2+66^2=x^2
sqrt11581 = x
107.6=x

Answer 5

So in order to find how much time it saves we have to change 7 miles per hour to 6 meters per hour?

Answer 6

Yes, that is the distance which you cut accross.
Now, how much distance does save you? You would have walked 85+66
without cutting,

so subtract *(85+66) - √[88²+65²]*

Answer 7

how many meters***

Answer 8

not 6

Answer 9

this in bold is the distance travelled in miles, and then divide by 7 to find the number of hours saved.

Answer 10

http://www.wolframalpha.com/input/?i=%28%2885%2B65%29-%E2%88%9A%2888%C2%B2%2B65%C2%B2%29%29%2F7

yes just a bit less than 6

Answer 11

So 5.799 hours saved?

Answer 12

Yes.

Answer 13

(If you would like we can do a by-hand approximation (I mean Taylor Polynomial) of the square root.....)

Answer 14

Wells this is an example problem from my engineering textbook. Was just wondering how to get the time saved, but why do we do *(85+66) - √[88²+65²]*

Answer 15

is it because 88+66 is the walking around the corner

Answer 16

and sqrt88^2+65^2 is the cut through?

Also why do we square this?

Answer 17

well, (85+66) miles is the distance that takes you to walk without cuttting across, correct?

Answer 18

Yes

Answer 19

And *√[88²+65²] miles* is the distance that takes you when you cut across.

Answer 20

So, the distance you saved by walking across is
(85+66) - √[88²+65²]

Answer 21

wait also where did the 88 come from?

Answer 22

Oh, typo

Answer 23

I apologize

Answer 24

88 should be 85

Answer 25

so that means that the hours saved would be 6.285

Answer 26

When you cut, you walk:
*√[85²+66²] miles*

Without cutting across
*(85+66) miles*

And then
*(85+66) - √[85²+66²] miles*
is the distance that you have saved by cutting across.

THEN, the time your have saved [knowing that you walk 7 miles per hour]
*( (85+66) - √[85²+66²] ) / 7*

Answer 27

Alright That makes a lot more sense putting it that way

Answer 28

6.19784932

Answer 29

yw