SOLUTION: The length of a tunnel was 22 1/2 times its width. If the length had been 50 feet less, it would have been 20 times the width. Find its length; its width.

Algebra ->  Rectangles -> SOLUTION: The length of a tunnel was 22 1/2 times its width. If the length had been 50 feet less, it would have been 20 times the width. Find its length; its width.      Log On


   

Question 468815: The length of a tunnel was 22 1/2 times its width. If the length had been 50 feet less, it would have been 20 times the width. Find its length; its width.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the tunnel's width
Let b = the tunnel's length
given:
(1) +b+=+22.5a+
(2) +b+-+50+=+20a+
---------------
Substitute b in (1) for b in (2)
(2) +22.5a+-+50+=+20a+
Add 50 to both sides
(2) +22.5a+=+20a+%2B+50+
Subtract +20a from both sides
(2) +2.5a+=+50+
(2) +25a+=+500%0D%0A%282%29+%7B%7B%7B+a+=+20+
And, since
(1) +b+=+22.5a+
(1) +b+=+22.5%2A20+
(1) +b+=+450+
The tunnel is 20 ft wide and 450 ft long
check answer:
(2) +b+-+50+=+20a+
(2) +450+-+50+=+20%2A20+
(2) +400+=+400+
OK