Calculate Average Speed: Converting 1½ km in 3 Minutes to Kilometers per Minute

Q: Why do I need to convert the mixed number to an improper fraction?

Converting $ 1\frac{1}{2} $ to $ \frac{3}{2} $ makes division much easier! It's hard to divide by a mixed number, but dividing fractions follows a clear rule.

Q: How do I divide by a whole number when I have a fraction?

When dividing $ \frac{3}{2} \div 3 $, treat 3 as $ \frac{3}{1} $, then multiply by the reciprocal: $ \frac{3}{2} \times \frac{1}{3} = \frac{3}{6} = \frac{1}{2} $

Q: What's the difference between speed and distance?

Speed tells you how fast something moves (km per minute), while distance tells you how far it traveled (total km). Speed always includes a time unit!

Q: Why is the answer smaller than the original distance?

That's normal! Joel ran $ 1\frac{1}{2} $ km in 3 minutes, so each minute he covered less than the total distance. Average speed per unit time is usually smaller than total distance.

Average Speed with Mixed Numbers

Joel ran $1\frac{1}{2}$ km in 3 minutes.

How many kilometers did Joel travel on average each minute?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find how many km Yoav traveled on average per minute

00:03 Divide the total km Yoav walked by the number of minutes

00:10 Convert mixed fraction to fraction

00:13 Any number divided by 1 always equals the number itself

00:26 Convert division to multiplication by reciprocal

00:39 Make sure to multiply numerator by numerator and denominator by denominator

00:46 Reduce the fraction as much as possible

00:57 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Joel ran $1\frac{1}{2}$ km in 3 minutes.

How many kilometers did Joel travel on average each minute?

Step-by-step solution

To find out how many kilometers Joel ran on average each minute, we begin with these steps:

Step 1: Convert the mixed number $1\frac{1}{2}$ km into an improper fraction. The mixed number represents 1 full unit plus half a unit, which is calculated as:

$1\frac{1}{2} = 1 + \frac{1}{2} = \frac{3}{2}$ km

Step 2: Use the average formula to calculate the distance per minute:

$\text{Average distance per minute} = \frac{\frac{3}{2} \text{ km}}{3 \text{ minutes}}$

Simplifying this expression involves dividing fractions:

$\frac{\frac{3}{2}}{3} = \frac{3}{2} \times \frac{1}{3} = \frac{3}{2 \times 3} = \frac{3}{6} = \frac{1}{2}$ km per minute

Therefore, Joel traveled, on average, $\frac{1}{2}$ km per minute. This matches the provided correct answer, confirming choice 4 is correct.

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Formula: Average speed equals total distance divided by total time
Technique: Convert $1\frac{1}{2}$ to improper fraction $\frac{3}{2}$
Check: Multiply answer by time: $\frac{1}{2} \times 3 = \frac{3}{2}$ km ✓

Common Mistakes

Avoid these frequent errors

Dividing time by distance instead of distance by time
Don't calculate 3 ÷ 1½ = 2! This gives minutes per kilometer, not kilometers per minute. Always divide total distance by total time to find average speed.

Practice Quiz

Test your knowledge with interactive questions

$2\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction?

Converting $1\frac{1}{2}$ to $\frac{3}{2}$ makes division much easier! It's hard to divide by a mixed number, but dividing fractions follows a clear rule.

How do I divide by a whole number when I have a fraction?

When dividing $\frac{3}{2} \div 3$ , treat 3 as $\frac{3}{1}$ , then multiply by the reciprocal: $\frac{3}{2} \times \frac{1}{3} = \frac{3}{6} = \frac{1}{2}$

What's the difference between speed and distance?

Speed tells you how fast something moves (km per minute), while distance tells you how far it traveled (total km). Speed always includes a time unit!

How can I check if my average speed answer makes sense?

Multiply your answer by the total time. You should get the original distance: $\frac{1}{2} \times 3 = \frac{3}{2} = 1\frac{1}{2}$ km ✓

Why is the answer smaller than the original distance?

That's normal! Joel ran $1\frac{1}{2}$ km in 3 minutes, so each minute he covered less than the total distance. Average speed per unit time is usually smaller than total distance.

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