1D Kinematics Legacy Problem #6 Guided Solution

As I read this problem, I begin to get a picture of a runner who's running for 20 minutes. And our runner is averaging a specific speed during the first 12.9 minutes of the run, and then a different speed during the last 7.1 minutes of this 20-minute run. And so the way I'm going to approach this question is I'm going to break it up into two phases of motion. The first phase, represented by the first time period, and then the second phase. And I want to calculate the total distance run in 20 minutes. So I'm going to find the distance run during the first section of time, and then during the second section of time, I'm simply going to add these two distances together. That will give me my answer. That's my strategy. That's how I approach things, and that's how any good problem solver is going to approach a physics problem, by getting a mental picture of what's going on, thinking about what's known and what we're looking for, and then thinking about strategy before we quickly pick up our calculator and start to calculate. So the quantities which are given are a distance, or rather a time, an average speed, and I'm looking for a distance. And so I'm going to simply use the average speed equal distance over time equation and rearrange that to be d equal d average times the time. Now the only other complication that I have in this problem is I have to give attention to some units, because this average speed is meters per second, and I'm multiplying that by time in minutes. That's just not going to work for me, so the way I'm going to approach that is before I actually go about doing my calculation of average speed times time, I'm going to get the time in the proper unit. I'm going to get it in units of seconds. So I've got to take my 12.9 minutes and my 7.1 minutes, and I have to multiply by 60 seconds per minute, and that's going to give me my time in seconds. Once I get those two times, I'm going to do my first calculation of distance for the first 12.9 minutes, 5.8 times 12.9. I'm going to repeat the same calculation with different numbers for the last 7.1 minutes. We get these two distances out of those calculations when I add them together.