Question

Tina bicycles for 2 hours at a constant speed, takes a break for 1 hour, and then continues to bicycle in the same direction for another

2 hours at the same speed she traveled previously. Which graph shows the total distance, d, in miles, Tina bicycles over t hours ?

Answer 1

Example

It took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?

Solution

We are given that it takes 1/2 an hour for the trip. This is a time:

t = 1/2

We are given that he averages 34 miles per hour. This is a rate:

r = 34

We are asked how few he has traveled. This is a distance. We use the d=rt equation:

d = rt

= (34)(1/2)

= 17

Markus lives 17 miles from work.

Answer 2

Explanation:

To solve this problem, we can use the formula:

distance = rate x time

Since Tina bicycles at a constant speed, we can simplify the formula to:

distance = speed x time

For the first 2 hours, Tina bicycles at a constant speed, so the distance she travels is:

distance = speed x time = s x 2

After taking a 1-hour break, Tina continues to bicycle at the same speed for another 2 hours, so the distance she travels is:

distance = speed x time = s x 2

Therefore, the total distance Tina travels over the 5-hour period is:

total distance = 2s + 2s = 4s

This means that the total distance Tina bicycles is directly proportional to the speed at which she travels. In other words, if Tina travels twice as fast, she will cover twice the distance in the same amount of time.

With this in mind, we can eliminate choices (A) and (B), which show linear relationships between distance and time. Since Tina is traveling at a constant speed, the graph of her distance should be a straight line with a positive slope.

Choice (C) shows a straight line with a positive slope, but the slope is too steep. This graph would indicate that Tina is traveling at a much faster speed than she actually is.

Choice (D) shows a straight line with a positive slope that is not as steep as (C). This graph accurately represents Tina's constant speed and shows the increase in distance after the break. Therefore, the correct graph is (D).