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Jennica is training for a marathon. During her training, she does 10km runs and they typically take her 1 hour ( 60 minutes) to complete. How long do you think it will take her to finish a full marathon (42km) ? Write down any assumptions you are making and show any calculations.

Jennica is training for a marathon. During her training, she does 10 km 10 \mathrm{~km} runs and they typically take her 11 hour ( 6060 minutes) to complete. How long do you think it will take her to finish a full marathon (42 km) (42 \mathrm{~km}) ? \newlineWrite down any assumptions you are making and show any calculations.

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Q. Jennica is training for a marathon. During her training, she does 10 km 10 \mathrm{~km} runs and they typically take her 11 hour ( 6060 minutes) to complete. How long do you think it will take her to finish a full marathon (42 km) (42 \mathrm{~km}) ? \newlineWrite down any assumptions you are making and show any calculations.
  1. Given Information: We are given that Jennica runs 10 km10\,\text{km} in 6060 minutes. We need to find out how long it will take her to run 42 km42\,\text{km}. We can set up a proportion to solve for the missing value, which is the time it will take to run 42 km42\,\text{km}. The proportion is based on the assumption that Jennica's running pace is constant.
  2. Set Up Proportion: First, we write down the known ratio of distance to time for Jennica's training runs: 10 km10\,\text{km} per 60 minutes60\,\text{minutes}. We then set up a proportion with the unknown time for the marathon, which we will call 'xx minutes', for the 42 km42\,\text{km} distance.\newline10 km60 minutes=42 kmx minutes\frac{10\,\text{km}}{60\,\text{minutes}} = \frac{42\,\text{km}}{x\,\text{minutes}}
  3. Cross-Multiply: Next, we solve for 'x' by cross-multiplying to find the equivalent time for 42 km42\,\text{km}. \newline(10 km)×(x minutes)=(42 km)×(60 minutes)(10\,\text{km}) \times (x\,\text{minutes}) = (42\,\text{km}) \times (60\,\text{minutes})\newline10x=42×6010x = 42 \times 60
  4. Solve for x: Now we perform the multiplication on the right side of the equation. 10x=252010x = 2520
  5. Convert to Hours: To find xx, we divide both sides of the equation by 1010.x=252010x = \frac{2520}{10}x=252x = 252
  6. Convert to Minutes: We have found that xx, the time it will take Jennica to run a full marathon, is 252252 minutes. However, it is often more useful to express this time in hours and minutes. To convert 252252 minutes into hours, we divide by 6060 (since there are 6060 minutes in an hour).252252 minutes ÷\div 6060 minutes/hour = 4.24.2 hours
  7. Final Answer: Since 0.20.2 hours is not a full hour, we need to convert this fraction of an hour back into minutes. To do this, we multiply 0.20.2 by 6060. \newline0.20.2 hours ×60\times 60 minutes/hour =12= 12 minutes
  8. Final Answer: Since 0.20.2 hours is not a full hour, we need to convert this fraction of an hour back into minutes. To do this, we multiply 0.20.2 by 6060. \newline0.20.2 hours ×60\times 60 minutes/hour =12= 12 minutes Adding the full hours and the additional minutes together, we find that Jennica will take 44 hours and 1212 minutes to finish a full marathon.

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