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The way to solve these problems is to reduce them to one linear equation with one unknown variable - speed, and then to solve this equation. When it is done, you can calculate the length of the trip. Problem 1. Motorboat moving upstream and downstream on a river A motorboat makes the 24 miles upstream trip on a river against the current in 3 hours. Returning trip with the current takes 2 hours.

Find the motorboat speed in still water and the current speed. Solution Let u be the motorboat speed in still water in miles per hour, and v be the current speed in miles per hour.

Thus you have the system of two linear equations in two unknowns. In the first equation divide both sides by 3. In the second equation divide both sides by 2. You will get an equivalent system. Add the first and the second equations. The motorboat speed in still water is equal to 10 miles per hour. The current speed is 2 miles per hour. Problem 2. Airplane flying into the wind and with the wind When an airplane flies into the wind, it can travel miles in 6 hours.

When it flies with the wind, it can travel the same distance in 5 hours. Find the speed of the airplane in still air and the speed of the wind. Solution Let u be the airplane speed in still air in miles per hour, and v be the speed of the wind in miles per hour.

Thus you have the system of two linear equations with two unknowns. In the first equation divide both sides by 6. In the second equation divide both sides by 5. The speed of the airplane in still air is equal to miles per hour. The speed of the wind is 50 miles per hour. Problem 3. Motorboat moving upstream and downstream on a river A motorboat makes an upstream trip on a river in 3 hours against the current, which is of 2 miles per hour.

The return downstream trip with the same current takes 2 hours. In this tutorial, you will see 5 important types of problems. At the end of the tutorial, you will find short online practice test. Let us begin the tutorial now. In this type, you will be finding speed of boat in still water i. You have to remember a very simple formula as shown below.

Find the speed of the boat in still water. Solution: From the question, you can write down the below values. You have to substitute the above values in the below formula. This type is similar to type 1. But there is one difference. Here you have to find speed of stream and not the speed of the boat. You have to use the below formula to find speed of stream. Example Question 2: A man rows downstream 30 km and upstream 12 km.

If he takes 4 hours to cover each distance, then the velocity of the current is:. Solution: In this question, downstream and upstream speeds are not given directly. Hence you have to calculate them first.

Step 3: Calculation of speed of stream You have to substitute values got in steps 1 and 2 in below formula to find the speed of the stream. In this type, you have to find distance of places based on given conditions. Below example will help you to understand better. If in a river running at 2 km an hour, it takes him 40 minutes to row to a place and return back, how far off is the place? The man rows to a particular place and comes back.

You have to calculate the distance of this place. Let this distance be X. See the below diagram to understand clearly. Man starts from A, travels to B and comes back. Therefore, above equation becomes,.

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