Part A
Answer: 360 miles
Reason:
The graph shows the highest point occurs when y = 360. After this point, the truck turns around to go back to the starting point (the warehouse perhaps).
In other words, the truck starts at y = 0 when it's at the warehouse. It travels 360 miles to reach the customer, which is represented as the highest point of the V shaped curve. This process takes 6 hours.
Then another 6 hours elapses when the truck drives back to the warehouse. We assume the same route is used, and similar traffic conditions occur for each leg of the trip.
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Part B
Answer: The truck
Reason:
The graph shows that the truck takes 12 hours to get back to the warehouse. We look at the x intercept because this is when the distance from the start is back to y = 0 again.
Now we need to find out how long the car takes on its trip.
We'll plug in y = 0 into the car's equation and solve for x.
y = -72|x-5| + 360
0 = -72|x-5| + 360
72|x-5| = 360
|x-5| = 360/72
|x-5| = 5
x-5 = ± 5
x-5 = 5 or x-5 = -5
x = 5+5 or x = -5+5
x = 10 or x = 0
x = 0 or x = 10
This tells us that the car is at the warehouse when x = 0 and when x = 10.
Therefore, the car takes 10 hours to do a round trip, and it's the faster vehicle.
