Train, Boats, and Streams Problems

Trains, boats, and streams are very common problems students find difficult. Learning these types of problems can be made easier with a little bit of preparation. These questions test how well you can use a diagram to solve trains, boats, and stream problems. Being able to draw a diagram is an important skill for mathematics. To get the answer, all you will need is to follow certain steps or ask yourself some questions about the picture to get your answer. Trains, boats, and stream problems also test the use of ratios and dividing numbers by zero. 

Boats and Streams

Many exams include problems where you have a boat travelling down a stream. The boat moves at a constant velocity, stopping when it hits rocks or banks. 

Here is an example problem:

A boat has to travel for 30 hours at 3 km/h along the river with no obstacles in its way. At what time does it end up at point A? 

This problem can be solved by using the definition of average velocity, which is the distance travelled divided by the time taken. This means the distance travelled is 3*30 = 90 km; therefore, we have to divide this number by the time is taken, which is 30 hours. This gives us 0.7, which can be rounded to 1.  

The boat has a constant velocity as it travels down the river to end up at point A at some time t.

Trains

Trains have an average speed of v, and a velocity at any point in time is given by v. 

All of these facts can help you solve problems quickly. 

Here is an example: 

A train travels from point A to point B at a constant speed of 20 km/h. When does it reach its destination? 

Answer: t = 20/v = 4 km. 

The train has a velocity at the end of the journey, so it reaches its destination 4 km after leaving point A.

The Concept Behind Train, Boats, and Stream Problems

The problems with Trains, boats, and streams ask you to work out how long it takes to travel between two cities, how far away they are, or some other similar question. The trick to solving problems with trains, boats, and streams is working out what the questions mean and what they want you to find.

The first thing you should do when solving trains, boats, and stream problems is to work out what the problem is asking for. Think about the problem and look at each part of it carefully. Explain what you think the problem wants you to find in plain English. 

Here is an example:

Where (the distance) is the easiest to start, as it is a very simple word that describes the place that someone might want to get to (in this case, Greenwich). The next step is working out what they want with Greenwich. Is it the time it takes to get there? The answer is yes. The last step is writing out what we know in maths and putting it in terms of variables (numbers).

Steps to solve Trains, Boats, and Stream Problems

Sometimes the “plain English” may not have completely given you everything you need to work out the trains, boats, and stream problem. In this case, follow the given steps

Step 1: Work out what that trains, boats, and stream problem means

Basically, this will come from solving step 2 – working out what you need to do.

Step 2: Work out what you need to do

What you should do for this is:

1. Write out the question word by word.
2. Write out a possible answer word by word (for example, for the first part of the question about where you might write “New York City.” That is not true, so change it. For example, if the problem said, “I must go from New York City to Chicago,” then that would mean “I must go from New York to Chicago”).
3. Match the words you wrote out in Step 2 with the questions.
4. Use what you have to make a new sentence that matches the problem.

Step 3: Write it out in maths and work out the answer

First, choose what you think is the easiest way to solve it (abbreviating, drawing, etc.). The only rule here is that it must be correct. If it isn’t, try another way.

Step 4: But is it right?

After you have worked out your answer, check that it answers the question. Remember, only choose one solution. If you find that your way is not the same as what they ask, try another way or go back to steps 1 and 2 and maybe change some words around after you have done it correctly.

Conclusion 

It is important to know what we are talking about when we say a particular thing. If you understand this, you can use time and distance to answer questions, which will be useful in real life. All the Trains, boats, and stream or river-related questions are based on time, distance, speed, and acceleration concepts which are pretty basic. By using general algebra, these problems can be solved easily.

The last part – using these problems in real life – is the most important. These kinds of math problems will appear again and again in your exams.