Distance/Time/Speed:

One of the most frequently encountered concepts in mathematics and problem solving specifically is the distance/time/speed formula.

This formula states that:

Let us consider a car travelling at an average velocity (or speed) of 60 miles per hour. That means that in 1 hour, it will travel a distance of 60 miles. What about two hours? Well, in the first hour, it will travel 60 miles and in the second hour, it will travel another 60 miles; therefore:

And in 2 hours, the car will travel 120 miles.

How far will the car travel in 3 hours?

Again, in the first hour, the car will travel 60 miles, in the second hour, it will travel another 60 miles and in the third and last hour, it will travel yet another 60 miles. We therefore add:

to calculate that the car will travel 180 miles in 3 hours. Instead of adding 60 miles 3 times, however, all we have to do is multiply 60 miles by 3 hours to get the same result and if you will check our formula at the top of the page:

You may think it is not necessary to bother with the formula, when you can add the sixty miles for the first hour and the sixty for the second hour, for example. What about a plane that will fly at a speed of 618 miles per hour for 13 hours? It will certainly be faster to multiply 618 by 13, than add 618 thirteen times (not to mention adding 13 618 times).

So, remember, if you know the average speed and the total time of travel, multiplying the speed by time will give you the total distance travelled!

What happens, when you know the total distance travelled and the average speed, but you don’t know how long the trip will take?

Well, if we know that:

then it must follow that:

and if you divide the distance travelled by the average speed, your result will be the time the trip will take.

Let us take a look at the above example of the plane, flying at a speed of 618 miles/hour and let us assume that the total distance flown is 6,798 miles. Using the above variation of our distance formula:

And we know the trip will take 11 hours.

By the same logic, if

It will also be true that:

In other words, if we know the total distance travelled and the total time the travel took, we can calculate the average speed by dividing the distance by time. In our airplane example:

And dividing the total distance of 6,798 miles by 11 hours it took to complete the trip will allow us to calculate the speed of 618 miles per hour.

These are the basics of the distance/speed/time formula and you will encounter many variations and permutations of this concept in future problems, such as:

How long will it take to drive from Toronto to Montreal, a distance of 500 km, if the car is travelling at a speed of 100 km/hr?

How fast would a car have to travel the distance of 500 km between Montreal and Toronto, in order to make the trip in 4 hours?

Two trains are travelling toward each other from two stations, 360 miles apart. The first train left at 10.00 AM and is travelling at 60 miles/hour. The second train left at 10.30 AM and is travelling at 50 miles per hour. At what time are they going to meet?

A Boeing 747 leaves New York for London and flies at a speed of 600 miles/hour. At the same time, an Airbus 318 leavesLondon, flying to New York at a speed of 560 miles/hour along the same route. How far apart are they going to be 15 minutes before they meet?

Cities A and B are 180 km apart. A truck leaves A at 12 PM and travels to B at a speed of 20 m/sec.At 12.30 PM a car leaves A for B and will travel at a speed of 90 km/hr. How far from B
will the car catch up with the truck?

For answers and step-by-step solutions to the above five example problems, please visit our website at www.mathsteps.com
and click on the FREE TRIAL button and then the BASIC MATH. The above five problems are featured in Level 2, problems #4 and #5 and Level 5, problem #1, #2 and #3, respectively. Have fun.