Question 507307: A water tank is being emptied so that the height y (in feet) of the water inside the tank decreases at a linear rate with time t measured in hours past 12 noon. If the height was 15ft at 1pm and 7.5ft at 6pm, find
(a)the equation relating y to t
(b)the height at 12 noon
(c)the total time required to empty the tank
Found 2 solutions by ankor@dixie-net.com, lwsshak3:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A water tank is being emptied so that the height y (in feet) of the water inside the tank decreases at a linear rate with time t measured in hours past 12 noon. If the height was 15ft at 1pm and 7.5ft at 6pm, find:
:
(a)the equation relating y to t
Find the slope, assign the given values as follows
t1=1; y1=15
t2=6; y2=7.5
m =  = -1.5 is the slope
Use the point/slope form: y-y1 = m(x-x1), x=t
y - 15 = -1.5(t - 1)
y - 15 = -1.5t + 1.5 + 15
y = -1.5t + 16.5; is the equation
:
(b)the height at 12 noon
that occurs when t=0; 16.5 ft
:
(c)the total time required to empty the tank
That occurs when y = 0
-1.5t + 16.5 = 0
-1.5t = -16.5
t = 
t = +11 hrs to empty the tank
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! A water tank is being emptied so that the height y (in feet) of the water inside the tank decreases at a linear rate with time t measured in hours past 12 noon. If the height was 15ft at 1pm and 7.5ft at 6pm, find
(a)the equation relating y to t
(b)the height at 12 noon
(c)the total time required to empty the tank
**
Since there is a straight line relationship between height of water and time (hours), you can use standard form of equation for a straight line which is: y=mx+b, m=slope, b=intercept
..
Between 1 and 6 pm, a period of 5 hours, the height dropped from 15 ft to 7.5 ft, which gives a slope of (15-7.5)/(1-6)=7.5/-5=-1.5ft/hr=m. You now have part of the equation completed, y=-1.5x+b. To find b, use one of the given points on the line,(1,15).
15=-1.5*1+b
15=-1.5+b
b=16.5
Equation:
y=-1.5x+16.5
ans:
(a)the equation relating y to t: f(t)=-1.5t+16.5
(b)the height at 12 noon: f(0)=-1.5*0+16.5=16.5ft
(c)the total time required to empty the tank:
set y=0, then solve for t
0=-1.5t+16.5
1.5x=16.5
t=11hrs
see graph below as a visual check on answers:
|
|
|
