A cat walks in a garden. The cat walks north a distance of three meters in a time of 12 seconds. The cat then stops for 18 seconds before walking another six meters north in a time of 15 seconds. What is the cat’s average speed?
In this question, we have a cat that is walking north in a garden. The cat begins by walking a distance of three meters north. And it takes 12 seconds to walk those three meters. We can draw out this section of the journey. It’s probably worth noting that our cartoon cat here is definitely not to scale. We are told that the cat then stops. It stands still for 18 seconds. It then walks another six meters north, taking a time of 15 seconds to cover this second distance. So we have now drawn the whole journey that the cat takes. The question is asking us to work out the average speed of the cat.
Average speed is defined as the total distance traveled divided by the total time taken to travel that distance. If we call the total distance 𝑑 subscript 𝑇, where 𝑇 stands for total, and the total time 𝑡 subscript 𝑇, then we can say that the average speed 𝑠 is given by 𝑑 subscript 𝑇 divided by 𝑡 subscript 𝑇. So in order to calculate the average speed, we first need to find the total distance traveled, 𝑑 subscript 𝑇, and the total time taken, 𝑡 subscript 𝑇.
The total distance traveled is given by the sum of the two distances walked by the cat, namely, three meters and six meters. So we can write that 𝑑 subscript 𝑇 is equal to three meters plus six meters. This gives us nine meters. The total time it takes to cover this distance is given by the sum of the times it takes to walk each section. So that’s the 12 seconds for the first section and the 15 seconds for the second one. But also we need to include the 18 seconds for which the cat stands still.
Remember that we’re interested in the total time that the cat takes. So that includes any time for which it has stopped in the middle of its journey. This total time, 𝑡 subscript 𝑇, is therefore given by 12 seconds plus 18 seconds plus 15 seconds. Doing the sum gives us 𝑡 subscript 𝑇 as 45 seconds.
Now that we have our values for the total distance, 𝑑 subscript 𝑇, and the total time, 𝑡 subscript 𝑇, we can substitute these values in to our equation for the average speed. Then, we have that the average speed is given by nine meters divided by 45 seconds. This gives us our answer that the average speed of the cat is 0.2 meters per second.