SOLUTION: A sailing race takes place on a 300m course. The second leg of the course is 100 m longer that the first and the third leg is 100 m longer than the second. How long is the second

Algebra ->  Equations -> SOLUTION: A sailing race takes place on a 300m course. The second leg of the course is 100 m longer that the first and the third leg is 100 m longer than the second. How long is the second      Log On


   

Question 24817: A sailing race takes place on a 300m course. The second leg of the course is 100 m
longer that the first and the third leg is 100 m longer than the second. How long is the second leg?
Neil is 4 years older that Andrea If Neil was twice as old as Andrea four years ago how old was Andrea?
Twicw the sum of two consecutive integers is 42. What are the two integers?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first be y
Let the second be x
Let the third be z
y+x+z=300
x=100+y
x-y=100 (1)

z=100+x
z-x=100 (2)

y+x+z=300
x-y=100 ---(1)
2x+z=400 (set 1)

z-x=100 (2) ---> multiply this equation by and add it to set 1

2x+z=400
2z-2x=200
3z=600
z=200

200-x=100
x=100
Hence the second one is 100m long.



2.
Neil = 4+x
Andrea = x

four years ago neil's age = 4+x-4
Andreas age four year ago = x-4
2(x-4)=4+x-4
-8+2x=x
x=8

8+4=12
Hence Neil is 12 and Andrea is 8.

3.Consective integers = x, x+1
2(x+x+1)=42
4x+2=42
4x=40
x=10
10+1=11

Hence the two consective integers are 10 and 11.
Paul.