# Using the Magic Triangle for Speed, Distance and Time (Compound Measures)

## Speed Triangle Video

Speed, distance and time can be calculated using a magic triangle. D (the distance) goes in the top of the triangle, S (speed) goes in the bottom left of the triangle and T (time) goes in the bottom right of the triangle.

If you want to calculate the speed cover up S in the triangle and you get S = D/T

If you want to calculate the time cover up T in the triangle and you get T = D/S

If you want to calculate the distance cover up D in the triangle and you get D = S×T

**Example 1**

A car covers a distance of 150 miles in 2 ½ hours. Calculate the average speed of the car in miles per hour.

Since you want the speed cover up S in your triangle and you get S = D/T

Next substitute D = 150 and T = 2.5 into the formula for speed:

S = D/T

S = 150/2.5 = 60mph

**Example 2**

A car is travelling at a constant speed of 80kmph. How many kilometres will the car cover if it keeps this speed for the next 3 hours and 15 minutes?

This time you need to work out the distance so D = S × T

Be careful with the time as it needs to rewritten in hours only. 15 minutes is ¼ hour (0.25) so 3 hours and 15 minutes is 3.25 hours.

Now substitute S = 80 and T = 3.25 into the formula for distance:

D = S ×T

= 80 × 3.25

= 260km

So the car travels 260km in 3 hours and 15 minutes.

**Example 3**

How long will it take Simon to jog a distance of 15 miles if Simon jogs at a steady speed of 6mph.

Here you need to calculate the time so T = D/S.

Now substitute D = 15 and S = 6 into the formula T = D/S

T = 15/6

T = 2.5 hours

So Simon will take 2 hours and 30 minutes to cover the distance.

## Questions & Answers

Three cities A,B,C are at equal distance from each other. A person travels from A to B at 30km/h; from B to C at 40 km/ h, C to A at 50 km/ h. What is the average speed?

Since the distances are equal just work out the average of the 3 numbers.

30 + 40 + 50 is 120, and 120 divided by 3 is 40km/h.

Helpful 12Is there a magic triangle for force, mass, and acceralation?

Yes, put F as the top, M in the bottom left and A in the bottom right.

Helpful 6What does t = mean?

t stands for time.

Helpful 3Why do you substitute the numbers?

Substitute just means put the numbers into the formula.

If you don't do this then you can't work out the answer!

Helpful 3How long does it take for a car to travel 23 miles at 80mph?

To work out the time divide the distance by the speed.

23 divided by 80 is 0.2875 hours.

If you want this in minutes multiply 0.2875 by 60 to give 17.25 minutes.

Helpful 2

## Comments

This really helped me when i was doing my science homework!! :-)

What would make this Hub that one extra step ahead is a video explaining this also.

Thanks for sharing this.

I think this Hub is a right little cracker, really enjoyed the way you have laid it out it makes it so much easier to understand, I think this one will help many that are in schools and colleges especially for there exams, voted up!

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