SOLUTION: 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

Question 1005123: 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 by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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?
--------------
z = k/x (k is some constant)
6 = k/3 --> k = 18
---
At x = 12:
z = k/x = 18/12
z = 1.5
==================
Or,
x*z = k
3*6 = x*12
x = 1.5
======================
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
z = k*x/y
9.5 = k*3/6 --> k = 19
--
What is the value of Z when X = 8, and Y = 12?
z = 19*8/12
z = 38/3
I keep getting 38/3 for this one and it's wrong.
It's not 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?
--
r = no wind speed
60/(r+5) = 30/(r-5)
Invert --> (r+5)/60 = (r-5)/30
r+5 = 2r-10
r = 15 mi/hr
------------------------------
Biking speed is not linearly affected by windspeed. The problem was worded in a manner that could be worked, tho.

RELATED QUESTIONS
I am having trouble with these long equations, I know how to do them but I keep getting... (answered by stanbon)

Tutor Please Help...This question is from a textbook and I keep getting different... (answered by Earlsdon,rapaljer)

my math teacher is literally horrible at teaching and every year 75% of his class fails... (answered by rodriguezh2)

Please help me with this I've never heard of these nor have I done these. Find the... (answered by stanbon,ewatrrr)

I keep getting this wrong, can someone help me, please? I would be grateful. Thanks so... (answered by mananth)

Problem #61 on p. 150 Chapter 2.1 reads - 2/3 - (- 5/8). We've done these before so I... (answered by tutorcecilia)

Hi! I'm in 8th grade and am struggling with Algebra 1. I am stuck on this one problem and (answered by rapaljer,elima)

Can someone please help me with this? I am confused and keep getting different answers.... (answered by ankor@dixie-net.com)

Hi, can you please help me? Ive tried this problem 9 times...and I keep getting it... (answered by ankor@dixie-net.com)