Uniform Motion Problems

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

1. An airplane can fly 900 miles in 3 hours when it’s traveling with the wind. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.
2. A speedboat is traveling along a river. When it’s going downstream, it can travel 120 miles in 4 hours. When it’s going upstream, it takes 5 hours to complete the return journey. Find the speedboat’s speed in still water and the speed of the current.
3. A man rode a snowmobile at the rate of 20 mph and then skied cross country at the rate of 6 mph. During the 6-hour trip, he traveled 57 miles. How long did he snowmobile, and how long did he ski?
4. A bicyclist headed east at a rate of 20 miles per hour. An hour later, her sister left the same spot in a car headed east at a rate of 60 miles per hour. How long will the bicyclist have been riding when her sister catches up to her?

(For some reason, there's a problem with the audio in portions of these videos. I hope to record new versions soon, but for now, you can still watch to see the steps.)