SOLUTION: 1. Jeff bicycles 160 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreaased his speed by 4 mph. Find r. 2. A box with no top is to b

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Question 353440: 1. Jeff bicycles 160 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreaased his speed by 4 mph. Find r.
2. A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 200 cubic inches. How large should the piece of metal be?
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
1. Jeff bicycles 160 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreaased his speed by 4 mph. Find r.

160/r= t
160/(r-4)-160/r = 2
LCM r(r-4)
160r-160(r-4)/r(r-4)=2
640= 2(r^2-4r)
320=r^2-4r
r^2-4r-320=0
r^2-20r+16r-320=0
r(r-20)+16(r-20)=0
(r+16)(r-20)=0
r= 20


2. A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 200 cubic inches. How large should the piece of metal be?
let metal sheet length be x. It is a square.
after cutting the dimensions become x-4 by x-4
V= L*W*H
(x-4)(x-4)*2 = 200
(x^2-8x+16)*2=200
x^2-8x+16=100
x^2-8x-84=0
x^2-14x+6x-84=0
x(x-14)+6(x-14)=0
(x-14)(x+6)=0
x= 14
14 by 14 inches
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m.ananth@hotmail.ca