Jon averages 30mph when he drives on the highway to his hous

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)

Solution

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)