Question 154463: please help me solve this problem in quadratic equation;
48.A rectangular plot of ground is 120 yards long and 80 yards wide.To double the area of the plot, while rataining the rectangular shape, strips of equal width will be added at one end and along one sde. Find the width of the strip?
49.A motorboat takes 4 hours to travel 30 miles downstream and then 18 miles upstream on a river whose current flows at the rate of 3 miles per hour. How fast can the boat travel in still water?
50.The floor of a basement game room is covered by 480 square asphalt tiles of a certain size. if 3 inches were added to the length of a side of each tile, the floor could be covered by 270 tiles. find the length of a side of the tile on the floor?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 48.A rectangular plot of ground is 120 yards long and 80 yards wide.To double the area of the plot, while retaining the rectangular shape, strips of equal width will be added at one end and along one side. Find the width of the strip?
:
See #154457
:
49.A motorboat takes 4 hours to travel 30 miles downstream and then 18 miles upstream on a river whose current flows at the rate of 3 miles per hour. How fast can the boat travel in still water?
:
Let s = boat speed in still water
then
(s+3) = speed downstream
and
(s-3) = speed upstream
:
Write a time equation: Time = dist/speed
:
Time upstream + Time downstream = 4 hrs
 +  = 4
Multiply the equation by the common denominator, (s+4)(s-4); results:
30(s-3) + 18(s+3) = 4(s+3)(s-3)
:
30s - 90 + 18s + 54 = 4(s^2 - 9)
:
48s - 36 = 4s^2 - 36
arrange as a quadratic equation:
4s^2 - 48s -36 + 36 = 0
4s^2 - 48s = 0
4s(s - 12) = 0
s = 12 mph boat in still water
;
Check solution; speed upstream 9 mph, downstream 15 mph; confirm the time:
(30/15) = 2
(18/9) = 2
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total = 4 hrs
:
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50.The floor of a basement game room is covered by 480 square asphalt tiles of a certain size. if 3 inches were added to the length of a side of each tile, the floor could be covered by 270 tiles. find the length of a side of the tile on the floor?
:
Let x = the side dimension of the original tile
then
(x+3) = the side dimension of the projected tile
:
That areas remain the same so we have:
480x^2 = 270(x+3) ^2
FOIL the right
480x^2 = 270(x^2 + 6x + 9)
:
480x^2 = 270x^2 + 1620x + 2430
Arrange as a quadratic on the left
480x^2 - 270x^2 - 1620x - 2430 = 0
:
210x^2 - 1620x - 2430 = 0
Simplify, divide equation by 30:
7x^2 - 54x - 81 = 0
Factor
(7x+9)(x-9) = 0
Positive solution:
x = 9 in, the side of the original tile
:
:
Check solution by finding the area of each scenario:
480(9^2) = 38880
270(12^2) = 38880
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