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?

Question

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.

Answer 1

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".

Answer 2

AAAaannndd the bot gets it wrong yet again!

Bus 124/2 = 62 mi/hr, so it is slower than Bus 1.