Algebra 2 help? So confused!

Question

Can someone please help me with these questions? I am so stuck and I keep getting the wrong answers. It would be greatly appreciated.

1.The variable Z is inversely proportional to X. When X is 3, Z has the value 6.What is the value of Z when X = 12?


2.The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 6, Z has the value 9.5.What is the value of Z when X = 8, and Y = 12? I keep getting 38/3 for this one and it's wrong.

3. On a particular day, the wind added 5 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 5 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 60 miles with the wind, he could go only 30 miles against the wind.What is his normal bicycling speed with no wind?


Even if you can only help with one, it would really help me out! Thanks for your time!

Answer 1

1. Z=(k/x) 

6 = (k/3) 

k=18

 

Z=(18/12)

Z=1.5

 

2. Z=(kx/y)

9.5=(3k/6)

k=19

 

Z=(19*8)/12

Z=12.667

 

I see this is the same answer you got (38/3), does it state whether it wants an improper fraction/decimal/mixed number?

 

3. d=r*t

t=d/r

 

With the wind: t=60/(r+5)

Against the wind: t=30/(r-5)

 

Set the equations equal to each other (can do this because they have the same time)

60/(r+5) = 30/(r-5)

Cross Multiply!

60(r-5)=30(r+5)

reduce

2(r-5)=r-5

simplify

2r-10=r-5

solve for r:

r=15!