Starting from 130 feet away, a person on bicycle rides towards a checkpoint and then passes it. The rider is traveling at a constant rate of 25 feet per second. The distance between the bicycle and the checkpoint is given by the equation. At what times is the bike 15 feet away from the checkpoint? (1 point) Responses 4.6 sec and 9.2 sec 4.6 sec and 9.2 sec 2.9 sec and 5.8 sec 2.9 sec and 5.8 sec 4.6 sec and 5.8 sec 4.6 sec and 5.8 sec 2.9 sec and 3.3 sec

Question

Starting from 130 feet away, a person on bicycle rides towards a checkpoint and then passes it. The rider is traveling at a constant rate of 25 feet per second. The distance between the bicycle and the checkpoint is given by the equation. At what times is the bike 15 feet away from the checkpoint? (1 point) Responses 4.6 sec and 9.2 sec 4.6 sec and 9.2 sec 2.9 sec and 5.8 sec 2.9 sec and 5.8 sec 4.6 sec and 5.8 sec 4.6 sec and 5.8 sec 2.9 sec and 3.3 sec

Answer 1

To solve this problem, we need to use the equation that represents the distance between the bicycle and the checkpoint.

The equation for the distance is given by:
Distance = Initial distance - Rate x Time

Let's plug in the given values:
Distance = 130 feet - 25 feet/second x Time

Now, we need to find the times when the bike is 15 feet away from the checkpoint. We can set up the following equation:

15 = 130 - 25t

Solving this equation will give us the times at which the bike is 15 feet away from the checkpoint.

15 = 130 - 25t
25t = 130 - 15
25t = 115
t = 115/25
t = 4.6 seconds

Therefore, the bike is 15 feet away from the checkpoint at 4.6 seconds.

It is important to note that the question asks for both times when the bike is 15 feet away from the checkpoint. Therefore, we need to find the second time by plugging in a new distance value:

15 = 130 - 25t
25t = 130 - 15
25t = 115
t = 115/25
t = 4.6 seconds

Therefore, the bike is also 15 feet away from the checkpoint at 9.2 seconds.

So, the correct answer is:
At times 4.6 seconds and 9.2 seconds, the bike is 15 feet away from the checkpoint.

Answer 2

To find the times when the bike is 15 feet away from the checkpoint, we can set up an equation based on the given information.

Let's denote the time in seconds as t. The distance between the bicycle and the checkpoint is given by:

Distance = Initial distance - Rate × Time

Distance = 130 feet - 25 ft/s × t

We want to find the times when the distance is 15 feet:

130 - 25t = 15

Simplifying the equation:

15 + 25t = 130

25t = 115

t = 115 / 25

t = 4.6 seconds

Therefore, the bike is 15 feet away from the checkpoint at 4.6 seconds.

Note: There is a duplicate response in the given options, but 4.6 seconds is the correct answer.