## 28 Apr Basic Concepts of Time, Speed and Distance

At Miracle Learning Centre, we teach you interesting stuff in math tuition. In one of our previous maths tuition, we had seen how to apply basic algebra in order to solve simple problems related to time, speed and distance. In this maths tuition, we are going further develop our understanding on the same topic and see how to apply algebra to solve some more difficult problems. Without any further delay, let us get started straight away.

**Average Speed**

This is a very common area of mistake. As a result, in this section of this math tuition, we are going to discuss how to compute the average speed.

So, consider the following problem. If you travel 100 kilometers at 25 kilometers/ hour and then travel another 100 kilometers at 20 kilometers/ hour, what is your average speed for the entire trip?

The formula for average speed goes as follows:

**Average speed, vavg = (Total Distance Covered)/(Total TimeTaken**)

So, in order to calculate the average speed, first we will have to figure out the total distance covered. In this case, the total distance covered = 100 + 100 = 200 kilometers.

Next, we are going to calculate the total time taken. The time taken for the first half of the trip:

t1 = 100/25 = 4 hours

The time taken for the second half of the trip:

t2 = 100/20 = 5 hours

So, total time taken = t = t1 + t2 = 4 + 5 = 9 hours.

As a result, the average trip for the entire trip = 200/9 = 22 2/9 kilometers/hours

**Problems involving trains**

Another popular set of problems related to time, speed and distance involves trains. In this section of this math tuition, we are going learn about the concepts which will help you to tackle these kinds of problems.

Let us discuss this with a sample problem. There is a tree just beside the railway tracks. How much time will a train which is 200 meters long and which is travelling at 10 meters/second, take to pass the tree?

The big idea for problems regarding trains is the fact that in order to pass something, the train must travel its own length plus the width of the object it is passing.

The width of the object the train is overtaking in this case, which is a tree, is negligible. As a result, we can simply calculate how long the train will take to cover a distance which is equal to its own length i.e. 200 meters in this case.

As a result, the time required = 200/10 = 20 seconds.

Now, suppose we are asked to calculate how long the same train above will take to pass platform which is 300 meters long.

In order to pass the platform completely, the train must cover a distance which is equal to the length of the train plus the length of the object which it has to pass i.e. the length of the platform.

As a result, the distance to be covered = 200 + 300 = 500 meters.

Therefore, required time to pass the platform = 500/10 = 50 seconds.

In this math tuition, we discussed two types of problems related to time, speed and distance and the related concepts using which we could tackle such problems. It is essential to have a solid understanding of the ideas discussed above in order to handle more complex problems related to time, speed and distance. As a result, it is extremely important that you have a thorough understanding of the above ideas. In case you face any difficulty in understanding any of the points discussed above, do not hesitate to talk to your teachers at math tuition or your peers. We hope you enjoyed this math tuition from Miracle Learning Centre. Look out for the next math tuition from Miracle Learning Centre.

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