### Video Transcript

A person walking strolls all the way around a pond, a distance of 12 meters. The person then turns around and walks six meters back around the pond. The person’s average speed is 0.9 meters per second. How much time does their walking take?

This question is about a person walking around a pond. We are told that they walk all the way around the pond and that this distance is 12 meters. Then they turn around and walk six meters back in the opposite direction around the pond. The question asks us to calculate how much time the person’s walking takes, given that their average speed is 0.9 meters per second. We should recall that average speed is defined as total distance traveled divided by the total time taken to travel that distance. If we call the average speed 𝑠, the total distance 𝑑, and the total time 𝑡, then we can write that 𝑠 is equal to 𝑑 divided by 𝑡.

We’re asked to calculate the time taken. So we should start by rearranging this equation to make 𝑡 the subject. To do this, we begin by multiplying both sides of the equation by 𝑡. Then the 𝑡’s in the numerator and the denominator on the right-hand side of this equation cancel out. Then we have that 𝑡 multiplied by 𝑠 is equal to 𝑑. The next step is to divide both sides of the equation by the speed 𝑠. This time, it’s on the left-hand side that we have the 𝑠’s in the numerator and the denominator canceling. We therefore have that total time 𝑡 is equal to total distance 𝑑 divided by average speed 𝑠.

The question has told us the average speed. This is 0.9 meters per second. So we can write that 𝑠 equals 0.9 meters per second. We’re not given the total distance traveled directly. We need to calculate this ourselves. This total distance is the sum of the first distance walked, the 12 meters all the way around the outside of the pond, and the second distance walked, the six meters back in the opposite direction. So we have that 𝑑 is equal to 12 meters plus six meters. This gives us a total distance 𝑑 of 18 meters.

Now we just need to substitute in our values for the average speed 𝑠 and the total distance traveled 𝑑 into our equation for the total time taken 𝑡. Doing this, we have that 𝑡 is equal to 18 meters divided by 0.9 meters per second. This gives us our answer that the time that the person’s walking takes is 20 seconds.