Consider the amount of gas in your car during a road trip. You start out with 45 gallons and drive for 4 hours, leaving you with 27 gallons in the tank. You stop for lunch for 2 hours and then drive for 2 more hours, leaving you with 18 gallons.
t= time
C (t)=_____ if 0 </ t </ 4
C (t)=_____ if 4 < t </ 6
C (t)=_____ if 6 < t </ 8
I'll do one:
C(t) = 45 - (45-27)/4 * 4 - (27-18)/2 * (t-6)
= 27 - 9/2 (t-6)
= 54 - 9/2 t if 6 < t <= 8
This should give a clue to the other parts...
45-4.5t
To find the amounts of gas at different times during the road trip, we can set up a linear equation based on the given information.
First, let's find the rate at which the gas is being consumed. We know that in 4 hours, the gas decreases from 45 gallons to 27 gallons. So, the rate of consumption can be calculated as (45 - 27) gallons / 4 hours = 18 gallons / 4 hours = 4.5 gallons/hour.
Now, we can set up the equation for the amount of gas at different time intervals:
1. For 0 ≤ t ≤ 4 (first 4 hours):
Since the rate of consumption is 4.5 gallons/hour, the equation can be written as:
C(t) = 45 - 4.5t
2. For 4 < t ≤ 6 (during the lunch break):
During the 2-hour lunch break, the gas consumption rate is zero. Therefore, the equation remains the same as the previous interval:
C(t) = 45 - 4.5t
3. For 6 < t ≤ 8 (remaining 2 hours):
We are given that at the end of these 2 hours, there are 18 gallons of gas remaining. Therefore, we can set up the equation as:
C(t) = 18 - 4.5(t - 6)
So, the equations for the amount of gas at different time intervals are:
C(t) = 45 - 4.5t for 0 ≤ t ≤ 4
C(t) = 45 - 4.5t for 4 < t ≤ 6
C(t) = 18 - 4.5(t - 6) for 6 < t ≤ 8