SOLUTION: I am helping my daughter with her homework and have no idea what I am doing, hope you can help. Gas tank problem. Suppose that you get your car's gas tank filled up, then drive

Question 109096: I am helping my daughter with her homework and have no idea what I am doing, hope you can help.
Gas tank problem. Suppose that you get your car's gas tank filled up, then drive off down the highway. As you drive, the number of minutes, t, since you had the tank filled and the number of liters, g, remaining in the tank are related by a linear function. After 30 minutes you have 59 liters left. An hour after the fill-up you have 38 liters left.
a) Which variable should be independent and which should be dependent?
b) Write the particular equation for this function.
c) Use the equation to predicit the time when you will run out of gas
d) Find the g-intercept and tell what it represents in the real world.
e) Tell what the slope represents in the real world, and tell the significance of the fact that the slope is negative.
f) sketch the graph.
Thank you I hope you can help me, Brian
Found 2 solutions by scott8148, edjones:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a) the amount of gas in the tank is dependent on the time

b) in the space of 30 min, you go from 59 liters to 38 lliters ... this -.7 liters/min is the slope
... when the tank was full (30 min before you had 59 liters) there would have been 59-30(-.7) or 80 liters
... g=-.7t+80

c) 0=-.7t+80 ... -80=-.7t ... 80/.7=t

d) g-intercept is 80 (see b) ... this represents the capacity of the tank

e) the slope is the rate of fuel consumption ... it is negative because the fuel is burned (consumed) over time

f) graph g on the vertical axis and t on the horizontal axis
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a) t is independent because the number of liters depend on how much time has gone by.
.
b) 59-38=21
59+21=80g full tank
using 21*2=42g/hr
g=80-42t (t is in hours)
.
c) 80-42t=0
-42t=-80
t=-80/-42
=1.905 hrs or 114.29 minutes
.
d) the g intercept occurs when t=0
When t=0 g=80 (0,80)
It represents a full tank.
.
e) The slope represents the rate at which the tank will empty.
The fact that is negative signifies that with time you will run out of gas.
.
This car is a real gas burner.
Ed

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