Question

lin rode her bike 2 miles in 8 minutes. she rode at a constant speed. complete the table to show the time it took her to travel different distances at this speed. what is the value of a in the table below?

distance traveled (miles)	elapsed time (minutes)
1	a
b	1

Explanation:

Step1: Find the speed ratio

Since speed is constant, distance and time are proportional. For 2 miles, time is 8 minutes. So the ratio of distance to time is constant. For distance 1 mile (half of 2 miles), time should be half of 8 minutes? Wait, wait, the first row has 2 miles and 81 minutes? Wait, maybe that's a typo? Wait, original problem: Lin rode 2 miles in 8 minutes. So maybe the first row is 2 miles and 8 minutes, not 81. Maybe a typo. Assuming that, then:

If 2 miles take 8 minutes, then 1 mile (which is half of 2 miles) will take half the time. So time for 1 mile is \( \frac{8}{2} = 4 \) minutes. Wait, but if the first row is 2 miles and 81 minutes, that would be different. But that must be a typo. So assuming the correct first row is 2 miles, 8 minutes.

Step2: Calculate time for 1 mile

Since distance and time are proportional (constant speed), the ratio of distance to time is constant. So \( \frac{2 \text{ miles}}{8 \text{ minutes}} = \frac{1 \text{ mile}}{a \text{ minutes}} \)

Cross-multiplying: \( 2 \times a = 1 \times 8 \)

So \( 2a = 8 \)

Divide both sides by 2: \( a = \frac{8}{2} = 4 \)

Answer:

4