Calculate Remaining Distance: Running 39km at 9km/h After 3 Hours

Q: Why can't I just say Ron has been running for 3 out of 4 hours so he has 25% left?

Time percentage and distance percentage are different things! Ron runs at constant speed, so you need to calculate the actual distance covered (27 km) and find what percent of 39 km that represents.

Q: How do I remember the distance formula?

Think of it like this: if you drive at 60 km/h for 2 hours, you go 120 km total. Distance = Speed × Time is just like finding the area of a rectangle!

Q: Should I round my percentage answer?

Yes! $ \frac{12}{39} \times 100 = 30.77\% $ rounds to 31%. Most percentage problems expect you to round to the nearest whole number unless told otherwise.

Q: What if the runner changes speed during the run?

This problem assumes constant speed of 9 km/h throughout. If speed changes, you'd need to calculate distance for each speed segment separately, then add them up.

Percentage Calculations with Distance and Time

Ron runs at a speed of 9 km/h and he plans to run a distance of 39 km.

So far, he has been running for 3 hours.

Approximately what percent of the route does Ron have left to run?

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Step-by-step written solution

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Understand the problem

Ron runs at a speed of 9 km/h and he plans to run a distance of 39 km.

So far, he has been running for 3 hours.

Approximately what percent of the route does Ron have left to run?

Step-by-step solution

To solve this problem, let's go through these steps:

Step 1: Calculate the distance Ron has already covered. Given his speed of 9 km/h and time of 3 hours:
$\text{Distance covered} = 9 \, \text{km/h} \times 3 \, \text{hours} = 27 \, \text{km}$
Step 2: Find the remaining distance Ron needs to run:
$\text{Remaining distance} = 39 \, \text{km} - 27 \, \text{km} = 12 \, \text{km}$
Step 3: Calculate the percentage of the route remaining:
$\text{Percentage remaining} = \left( \frac{12 \, \text{km}}{39 \, \text{km}} \right) \times 100 \approx 30.77\%$

Therefore, rounding to the nearest whole number, approximately 31% of Ron's running route remains.

Final Answer

31%

Key Points to Remember

Essential concepts to master this topic

Formula: Use distance = speed × time to find covered distance
Technique: Subtract covered distance from total: 39 - 27 = 12 km remaining
Check: Verify percentage: $\frac{12}{39} \times 100 = 30.77\% \approx 31\%$ ✓

Common Mistakes

Avoid these frequent errors

Converting time percentage instead of distance percentage
Don't calculate 3/4 hours as 75% and think that's the answer! Time percentage doesn't equal distance percentage when speed is constant. Always find the actual distance covered first, then calculate what percentage of the total route remains.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{11}{50}$ written as a percentage?

FAQ

Everything you need to know about this question

Why can't I just say Ron has been running for 3 out of 4 hours so he has 25% left?

Time percentage and distance percentage are different things! Ron runs at constant speed, so you need to calculate the actual distance covered (27 km) and find what percent of 39 km that represents.

How do I remember the distance formula?

Think of it like this: if you drive at 60 km/h for 2 hours, you go 120 km total. Distance = Speed × Time is just like finding the area of a rectangle!

Should I round my percentage answer?

Yes! $\frac{12}{39} \times 100 = 30.77\%$ rounds to 31%. Most percentage problems expect you to round to the nearest whole number unless told otherwise.

What if the runner changes speed during the run?

This problem assumes constant speed of 9 km/h throughout. If speed changes, you'd need to calculate distance for each speed segment separately, then add them up.

How can I check if 31% is reasonable?

Quick check: Ron covered 27 km out of 39 km, so he's done about 70% of the route. That leaves about 30% remaining, which matches our 31% answer!

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