Question

matteo spends a total of 38 min exercising. he walks for 6 min to warm up and then runs at a constant rate of 8 min per mile for the rest of the time. matteo says that he ran 4.75 mi. is he correct? explain your reasoning.

Explanation:

Step1: Find running time

Total exercise time is 38 min, warm - up (walking) time is 6 min. So running time $t = 38 - 6=32$ min.

Step2: Calculate miles run

Running rate is 8 min per mile. Let the number of miles be $m$. The time taken to run $m$ miles is $8m$ minutes. We know running time is 32 min, so $8m = 32$. Solving for $m$, we divide both sides by 8: $m=\frac{32}{8} = 4$. Wait, but let's check with the claim of 4.75 miles. Wait, maybe I misread. Wait, the rate is 8 min per mile, so time per mile is 8 min. So miles = running time / 8. Running time is 38 - 6 = 32 min. So miles = 32/8 = 4. But wait, maybe the rate is 8 miles per minute? No, that doesn't make sense. Wait, 8 min per mile means for each mile, it takes 8 minutes. So if he runs for $t$ minutes, miles $m=\frac{t}{8}$. $t = 38 - 6=32$. So $m = 32/8 = 4$. But Matteo says 4.75. Wait, maybe I made a mistake. Wait, 38 - 6 is 32? No, 38 - 6 is 32? Wait, 38 minus 6 is 32? Yes. Then 32 divided by 8 is 4. So he ran 4 miles, not 4.75. Wait, but let's recalculate. Wait, maybe the total time is 38, warm - up 6, so running time 32. 32 minutes at 8 minutes per mile: 32/8 = 4. So Matteo is incorrect. Wait, but maybe the rate is 8 miles per minute? No, that would be too fast. Wait, maybe the problem is 8 miles per hour? No, the problem says 8 min per mile. So according to the calculation, he ran 4 miles, so his claim of 4.75 is wrong. Wait, but let's check again. Wait, 38 - 6 = 32. 32 divided by 8 is 4. So the correct number of miles is 4, so Matteo is incorrect.

Answer:

Matteo is incorrect. The total exercise time is 38 minutes, with 6 minutes for warm - up, so the running time is \(38 - 6=32\) minutes. Since the running rate is 8 minutes per mile, the number of miles run is \(\frac{32}{8} = 4\) miles, not 4.75 miles.