Two freight trucks are traveling to the same destination, and each are traveling at a constant speed. Truck A is 187 miles away from its destination at 9 a.m., one hour after leaving from its origin, and is 99 miles away from the destination at 10:36 a.m. Truck B started traveling to its destination at 6:30 a.m. Truck B is 248 miles away at 8:30 a.m. and 155 miles away at 10 a.m. Analyze each situation to determine a function that finds the distance to the destination for each truck based on the time in hours after starting the trip from the origin to the destination. Then use the functions to determine which truck will arrive first to its destination.
To analyze the situations and determine the functions for the distance to the destination for each truck based on time, we can use the given information to create equations.
Let's start with Truck A:
- At 9 a.m., one hour after leaving its origin, Truck A is 187 miles away from the destination.
- At 10:36 a.m., Truck A is 99 miles away from the destination.
We can calculate the time elapsed between these two points:
10:36 a.m. - 9 a.m. = 1 hour and 36 minutes = 1.6 hours
Now, we can set up the equation for Truck A:
Distance = Speed * Time + Initial Distance
Let's assume Truck A's speed is "x" miles per hour and its initial distance is 187 miles at 9 a.m.
Using the equation, we can write:
99 miles = x × 1.6 hours + 187 miles
Simplifying the equation, we get:
99 = 1.6x + 187
By rearranging the equation, we can isolate "x" (Truck A's speed):
1.6x = 99 - 187
1.6x = -88
x = -88 / 1.6
x = -55
Since speed cannot be negative, there seems to be a mistake in the given information or calculations, as negative speed is not possible in this scenario.
Now let's move on to Truck B:
- At 8:30 a.m., Truck B is 248 miles away from the destination.
- At 10 a.m., Truck B is 155 miles away from the destination.
We can calculate the time elapsed between these two points:
10 a.m. - 8:30 a.m = 1.5 hours
Using the same equation for distance, we have:
Distance = Speed * Time + Initial Distance
Assuming Truck B's speed is "y" miles per hour and its initial distance is 248 miles at 8:30 a.m., we can write:
155 miles = y × 1.5 hours + 248 miles
Simplifying the equation, we get:
155 = 1.5y + 248
By rearranging the equation, we can isolate "y" (Truck B's speed):
1.5y = 155 - 248
1.5y = -93
y = -93 / 1.5
y = -62
Again, we encounter negative speed, which is not possible. Therefore, there seems to be an error in the given information or calculations for both cases.
Without the correct speeds for each truck, we cannot determine which truck will arrive first at its destination.