Question 1200: Jon averages 30mph when he drives on the highway to his house and 50mph on the interstate. If both routes are the same length, and he saves 2 hours by traveling on the interstates, how far away is his house?
A farmer has 300ft of fencing and wants to enclose a rectangular area of 500ft square. What dimensions should he use? (p=2l+2w, A=l*w)
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Sol: (i) Assume the time if he drives on the interstate is x hrs,then it takes x+2
for him to drive on highway.
Since both routes are the same length,we have
50x = 30(x+2)
or 50x = 30x + 60,
or 20 x = 60, so x = 3 (hrs)
Hence,the required distance is 50*3= 150 miles.
(ii) Assume the dimensions are L& W,we have
2L+ 2 W = 300 or L + W = 150...(1)
and LW = 500...(2)
By (1): L = 150-W, in (2),replace L by 150-W,we have
(150 - W)W = 500,
So, W^2 -150 W + 500 = 0,
By quadratic formula,we obtain W= 75+ 5sqrt(205) =146.59
or 75- 5sqrt(205) = 3.41.
And so,we have the correponding
L= 150 -W = 150-(75+ 5sqrt(205)) = 75- 5sqrt(205)
or L= 150 -W = 150-(75 - 5sqrt(205)) = 75 + 5sqrt(205)
Answer: the dimensions of the rectangle are 75- 5sqrt(205) and 75+ 5sqrt(205)
|
|
|
