For this case we have the following situation:
The monthly cost of a gym in the city is $ 3. The initial registration is $ 25. Write a mathematical expression that models the problem.
So we have to define variables:
x: number of months
y: total cost
The mathematical expression that models the problem is:
d = distance between the two cities
v₁ = average speed while going from chicago to kansas city = 440 knots
t₁ = time taken to travel distance going from chicago to kansas city
time taken to travel distance going from chicago to kansas city is given as
t₁ = d/v₁
t₁ = d/440 eq-1
v₂ = average speed while going from kansas city to chicago = 110 knots
t₂ = time taken to travel distance going from kansas city to chicago
time taken to travel distance going from kansas city to chicago is given as
t₂ = d/v₂
t₂ = d/110 eq-2
Given that :
t₂ = t₁ + 3
using eq-1 and eq-2
(d/110) = (d/440) + 3
d = 440
3
x
+
2
y
>
24
3
x
+
2
y
>
24
Solve for
y
y
.
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y
>
−
3
x
2
+
12
y
>
-
3
x
2
+
12
Use the slope-intercept form to find the slope and y-intercept.
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Slope:
−
3
2
-
3
2
Y-Intercept:
12
12
Graph a dashed line, then shade the area above the boundary line since
y
y
is greater than
−
3
x
2
+
12
-
3
x
2
+
12
.
y
>
−
3
x
2
+
12
y
>
-
3
x
2
+
12
Lets say, for ease, that the vat can hold a total of 70 gallons (or whatever you would like to use.) Use whatever number you want, I just picked this because it gives us a lot of clean numbers.
Now, if the inlet can fill it in 7 hours, that means that it is adding 10 gallons per hour. (70 gal/7 hours = 10 gal/hr)
For the outlet, use the same process, and you find that it drains the vat at 7 gallons per hour.
So, if you subtract the outlet from the inlet, you get 10 - 7 = 3 gallons per hour added.
Now just divide the size of the vat by that number, and you find your answer.
70 gallons / 3 gallons per hour = 23 1/3 hours.
