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

*Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.*

## How to Use the Magic Triangle

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 traveling 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 be rewritten in hours only. 15 minutes is ¼ hour (0.25) so 3 hours and 15 minutes become 3.25 hours.

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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

**Question:** How long does it take for a truck to travel 30 miles at 5mph?

**Answer:** Divide the distance by the speed to give the journey length.

30 divided by 5 gives 6 hours.

**Question:** 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?

**Answer:** 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.

**Question:** Is there a magic triangle for force, mass, and acceralation?

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

**Question:** What does t = mean?

**Answer:** t stands for time.

**Question:** Why do you substitute the numbers?

**Answer:** Substitute just means put the numbers into the formula.

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

**Question:** How long does it take for a car to travel 23 miles at 80mph?

**Answer:** 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.

**Question:** Whats the whole triangle called?

**Answer:** The triangle is called the speed triangle.

**Question:** How fast must a car go to cover the distance of 224km in 2 hours and 20 min?

**Answer:** To work out the speed divdide the distance by the time.

2 hours and 20 minutes is 2 hours and 1/3 (or 2.3 recurring).

So 224 divided by 2.3 recurring is 96 km/h.

## Comments

**Ella** on May 10, 2013:

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

**happyturtle** from UK on February 09, 2012:

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

Thanks for sharing this.

**markbennis** on February 09, 2012:

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!