Question

a runners speed during a race is: 5 mph for the first 2 miles, then 4 mph for the next 3 miles. how long did the runner take to run the first 2 miles? chart: distance (miles) vs time (min), with points at (0,0), (10,2), (25,3) options: 5 min, 25 min, 10 min, 15 min

Explanation:

Step1: Recall the formula for time

The formula that relates speed (\(v\)), distance (\(d\)) and time (\(t\)) is \(t=\frac{d}{v}\). Here, the speed \(v = 5\) mph and the distance \(d=2\) miles.

Step2: Calculate the time in hours

Substitute the values into the formula: \(t=\frac{2}{5}\) hours.

Step3: Convert hours to minutes

We know that 1 hour = 60 minutes. So, to convert \(\frac{2}{5}\) hours to minutes, we multiply by 60: \(t=\frac{2}{5}\times60\) minutes.
Calculate \(\frac{2}{5}\times60=\frac{120}{5} = 24\)? Wait, no, wait the graph. Wait, maybe I made a mistake. Wait the graph: at distance 2 miles, the time is 10 minutes? Wait, maybe the speed - time - distance. Wait, speed is 5 mph. Let's re - calculate.

Wait, speed \(v = 5\) miles per hour. Distance \(d = 2\) miles. Time \(t=\frac{d}{v}=\frac{2}{5}\) hours. To convert to minutes, \(\frac{2}{5}\times60 = 24\) minutes? But the graph shows that at distance 2 miles, the time is 10 minutes. Wait, maybe I misread the speed. Wait the problem says "5 mph for the first 2 miles". Wait, maybe the graph is a distance - time graph. Let's look at the graph: the first segment goes from (0,0) to (10,2). So when distance is 2 miles, time is 10 minutes. Let's check with the formula. If time is 10 minutes, that is \(\frac{10}{60}=\frac{1}{6}\) hours. Speed \(v=\frac{d}{t}=\frac{2}{\frac{1}{6}}=12\) mph? No, that contradicts. Wait, maybe the problem is using the graph. The graph has distance on y - axis (miles) and time on x - axis (minutes). At distance 2 miles, the x - coordinate (time) is 10. So the answer is 10 minutes. Let's check with the formula again. Wait, maybe the speed is 12 mph? No, the problem says 5 mph. Wait, maybe there is a mistake in my calculation. Wait, 5 miles per hour means in 1 hour (60 minutes) the runner runs 5 miles. So to run 1 mile, it takes \(\frac{60}{5}=12\) minutes per mile. Then for 2 miles, it takes \(2\times12 = 24\) minutes? But the graph shows 10 minutes. Wait, maybe the problem's graph is correct, and I misread the speed. Wait the problem says "5 mph for the first 2 miles". Wait, maybe the question is based on the graph. The graph: distance (y) vs time (x). The first point after (0,0) is (10,2), so when distance is 2 miles, time is 10 minutes. So the answer is 10 minutes.

Wait, maybe my initial formula application was wrong. Let's re - express speed in miles per minute. 5 miles per hour is \(\frac{5}{60}=\frac{1}{12}\) miles per minute. Then time to run 2 miles is \(t=\frac{d}{v}=\frac{2}{\frac{1}{12}}=24\) minutes. But the graph shows 10 minutes. There is a contradiction. Wait, maybe the speed is 12 mph? No, the problem says 5 mph. Wait, maybe the question is a trick question based on the graph. The graph shows that at distance 2 miles, the time is 10 minutes (x - axis is time in minutes, y - axis is distance in miles). So the answer is 10 minutes.

Answer:

10 min