Consider two buses departing at the same time. For every hour t, Bus 1 will have traveled f(t) = 64t miles, while Bus 2 travels at a constant speed and goes 124 miles in the first 2 hours. At 6 hours, which statement is true?
Responses
Bus 1 will travel farther than Bus 2.
Bus 1 will travel farther than Bus 2.
none of these
none of these
Bus 2 will travel farther than Bus 1
Bus 2 will travel farther than Bus 1
Bus 1 and Bus 2 will travel the same distance.
Bus 1 and Bus 2 will travel the same distance.
AAAaannndd the bot gets it wrong yet again!
Bus 124/2 = 62 mi/hr, so it is slower than Bus 1.
To determine which statement is true, we need to compare the distances traveled by Bus 1 and Bus 2 at 6 hours.
For Bus 1, we can use the given function f(t) = 64t to find its distance at 6 hours:
f(6) = 64 * 6 = 384 miles
For Bus 2, we know it travels at a constant speed and covers 124 miles in the first 2 hours. Since the speed is constant, we can calculate its speed using the given distance and time:
Speed = Distance / Time = 124 miles / 2 hours = 62 miles/hour
Using this constant speed, we can find the distance traveled by Bus 2 in 6 hours:
Distance = Speed * Time = 62 miles/hour * 6 hours = 372 miles
Comparing the distances, we find that Bus 1 will travel farther than Bus 2 (384 miles > 372 miles). Therefore, the correct statement is: Bus 1 will travel farther than Bus 2.
To determine which bus will travel farther at 6 hours, we need to calculate the distance traveled by each bus.
For Bus 1, the distance traveled is given by the function f(t) = 64t. We can substitute t = 6 into the function to find the distance traveled by Bus 1 at 6 hours:
f(6) = 64 * 6 = 384 miles
For Bus 2, we are told that it travels at a constant speed and goes 124 miles in the first 2 hours. Since it travels at a constant speed, we can assume that it will continue to travel at the same speed throughout. So, in 6 hours, Bus 2 will travel:
124 miles + additional distance in the remaining 4 hours
To find the additional distance, we can use the formula distance = speed * time. We know that Bus 2 travels 124 miles in 2 hours, so its speed is 124 miles / 2 hours = 62 miles/hour. Using this speed, we can find the additional distance in the remaining 4 hours:
additional distance = speed * time
additional distance = 62 miles/hour * 4 hours = 248 miles
Adding the initial distance of 124 miles to the additional distance of 248 miles, we get the total distance traveled by Bus 2 at 6 hours:
124 miles + 248 miles = 372 miles
Comparing the distances traveled, we see that Bus 1 will travel farther than Bus 2.
Therefore, the correct statement is: Bus 1 will travel farther than Bus 2.
Explanation:
For Bus 1, we can use the given function f(t) = 64t to find how far it travels in 6 hours: f(6) = 64(6) = 384 miles.
For Bus 2, we know that it traveled 124 miles in the first 2 hours, leaving 4 more hours to travel. Since its speed is constant, we can use the formula distance = speed × time. Let's call the speed of Bus 2 "s". Then, in the remaining 4 hours, Bus 2 travels:
distance = speed × time = s × 4
We don't have enough information to find s, so we can't calculate the exact distance traveled by Bus 2. However, we can make a general statement: if Bus 2's constant speed is greater than 31 miles per hour (which would make its total distance traveled greater than 124 + 31 × 4 = 248 miles), then Bus 2 will travel farther than Bus 1. Otherwise, Bus 1 will travel farther.
Since we don't know the exact speed of Bus 2, the correct answer is "none of these".