Swimming Speed Calculation: Comparing 50m/25s vs 75m/50s Pace Analysis

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

Speed is distance ÷ time (how far you go per second). Pace is time ÷ distance (how long each meter takes). For pace, smaller numbers mean faster!

Q: Why is 0.5 seconds per meter faster than 0.67 seconds per meter?

Think of it this way: if it takes you 0.5 seconds to swim one meter versus 0.67 seconds, you're clearly faster in the first case! Less time per meter = faster pace.

Q: Do I need to convert all times to the same unit?

No! Since we're comparing ratios, the units cancel out. Just make sure you're consistent: all times in seconds and all distances in meters.

Q: What if two swimmers have the same pace?

That means they swim at exactly the same rate! In this problem, Swimmers A and C both have 0.5 seconds per meter, so they're tied for fastest.

Q: Can I use decimals or should I keep fractions?

Fractions: $ \frac{25}{50} = \frac{1}{2} $ (exact)Decimals: 0.5 or 0.67 (easier to compare)Both work, but decimals make ranking easier!

Q: How do I remember which swimmer is which after calculating?

Make a simple list as you calculate: A = 0.5, B = 0.67, C = 0.5, D = 0.8. Then rank from smallest to largest pace for fastest to slowest order.

Rate Calculations with Time-Distance Comparisons

During a swimming contest, four swimmers completed different distances in varying times:

Swimmer A - 50m in 25 seconds.

Swimmer B - 75m in 50 seconds.

Swimmer C - 20m in 10 seconds.

Swimmer D - 100m in 80 seconds.

Which swimmer had the fastest pace?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

During a swimming contest, four swimmers completed different distances in varying times:

Swimmer A - 50m in 25 seconds.

Swimmer B - 75m in 50 seconds.

Swimmer C - 20m in 10 seconds.

Swimmer D - 100m in 80 seconds.

Which swimmer had the fastest pace?

Step-by-step solution

First calculate the pace for each swimmer. Pace is the time taken per meter.

Swimmer A pace: $\frac{25}{50} = 0.5$

Swimmer B pace: $\frac{50}{75} \approx 0.67$

Swimmer C pace: $\frac{10}{20} = 0.5$

Swimmer D pace: $\frac{80}{100} = 0.8$

Swimmers A and C have the fastest pace at 0.5 seconds per meter. After them swimmer B and last swimmer D.

Final Answer

Swimmer D
Swimmer A
Swimmer C
Swimmer B

Key Points to Remember

Essential concepts to master this topic

Rate Formula: Pace = time ÷ distance gives seconds per meter
Technique: Calculate each pace: $\frac{25}{50} = 0.5$ seconds per meter for Swimmer A
Check: Fastest pace means lowest number: 0.5 < 0.67 < 0.8 ✓

Common Mistakes

Avoid these frequent errors

Confusing speed with pace by using distance ÷ time
Don't calculate distance ÷ time thinking higher numbers mean faster = wrong ranking! This gives speed (meters per second), but pace requires time ÷ distance. Always use time ÷ distance for pace comparisons.

Practice Quiz

Test your knowledge with interactive questions

What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

What's the difference between speed and pace?

Speed is distance ÷ time (how far you go per second). Pace is time ÷ distance (how long each meter takes). For pace, smaller numbers mean faster!

Why is 0.5 seconds per meter faster than 0.67 seconds per meter?

Think of it this way: if it takes you 0.5 seconds to swim one meter versus 0.67 seconds, you're clearly faster in the first case! Less time per meter = faster pace.

Do I need to convert all times to the same unit?

No! Since we're comparing ratios, the units cancel out. Just make sure you're consistent: all times in seconds and all distances in meters.

What if two swimmers have the same pace?

That means they swim at exactly the same rate! In this problem, Swimmers A and C both have 0.5 seconds per meter, so they're tied for fastest.

Can I use decimals or should I keep fractions?

Fractions: $\frac{25}{50} = \frac{1}{2}$ (exact)
Decimals: 0.5 or 0.67 (easier to compare)

Both work, but decimals make ranking easier!

How do I remember which swimmer is which after calculating?

Make a simple list as you calculate: A = 0.5, B = 0.67, C = 0.5, D = 0.8. Then rank from smallest to largest pace for fastest to slowest order.

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