5.MDR. 7 A runner completed a marathon that was 42,195 meters long. If the runner maintained the same speed of 10 kilometers per hour, how long did it take to complete the race? (HINT: 2 steps)

To solve the problem, we need to determine how long it took the runner to complete a marathon of 42,195 meters while maintaining a speed of 10 kilometers per hour. We'll follow these steps: ### Step 1: Convert the distance from meters to kilometers. The distance of the marathon is given in meters, and we need to convert it to kilometers since the speed is in kilometers per hour. \[ \text{Distance in kilometers} = \frac{\text{Distance in meters}}{1000} \] ### Step 2: Calculate the time taken to complete the marathon. We can use the formula for time, which is: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \] Now, let's perform the calculations for both steps. 1. Convert 42,195 meters to kilometers. 2. Calculate the time taken using the speed of 10 kilometers per hour. Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(\frac{42195}{1000}\) - step1: Reduce the fraction: \(\frac{8439}{200}\) Calculate or simplify the expression \( 42195 / (10 * 1000 / 3600) \). Calculate the value by following steps: - step0: Calculate: \(\frac{42195}{\left(\frac{10\times 1000}{3600}\right)}\) - step1: Remove the parentheses: \(\frac{42195}{\frac{10\times 1000}{3600}}\) - step2: Reduce the fraction: \(\frac{42195}{\frac{25}{9}}\) - step3: Multiply by the reciprocal: \(42195\times \frac{9}{25}\) - step4: Reduce the numbers: \(8439\times \frac{9}{5}\) - step5: Multiply: \(\frac{8439\times 9}{5}\) - step6: Multiply: \(\frac{75951}{5}\) ### Step 1: Convert the distance from meters to kilometers The distance of the marathon is: \[ \text{Distance in kilometers} = \frac{42195}{1000} = 42.195 \text{ kilometers} \] ### Step 2: Calculate the time taken to complete the marathon Using the speed of 10 kilometers per hour, we can calculate the time taken: \[ \text{Time} = \frac{42.195 \text{ km}}{10 \text{ km/h}} = 4.2195 \text{ hours} \] To convert this into a more understandable format, we can express it in hours and minutes. 1. The whole number part (4 hours) remains as is. 2. To find the minutes, we take the decimal part (0.2195 hours) and convert it to minutes: \[ 0.2195 \text{ hours} \times 60 \text{ minutes/hour} \approx 13.17 \text{ minutes} \] Thus, the time taken to complete the marathon is approximately **4 hours and 13 minutes**. ### Final Answer The runner took approximately **4 hours and 13 minutes** to complete the marathon.