Breanne and Alison finished a 5 km fun run. Alison finished 400 m ahead of Breanne. Breanne ran at an average speed of 7.2 km/h.What was Alison’s time for the race if she ran at a constant rate for the whole race?
Question
Breanne and Alison finished a 5 km fun run. Alison finished 400 m ahead of Breanne. Breanne ran at an average speed of 7.2 km/h.What was Alison’s time for the race if she ran at a constant rate for the whole race?
Solution
Step 1: Convert all distances to the same unit. In this case, we'll convert kilometers to meters because the difference in distance is given in meters. So, 5 km = 5000 m.
Step 2: Calculate the distance Breanne ran. Since Alison finished 400 m ahead of Breanne, Breanne ran 5000 m - 400 m = 4600 m.
Step 3: Calculate the time it took for Breanne to finish the race. We know that speed = distance/time. So, time = distance/speed. Breanne's speed is given in km/h, so we need to convert it to m/s. 7.2 km/h = 2 m/s (approximately). So, Breanne's time = 4600 m / 2 m/s = 2300 seconds.
Step 4: Calculate Alison's speed. We know that Alison ran 5000 m in the same time that Breanne ran 4600 m. So, Alison's speed = 5000 m / 2300 s = 2.17 m/s (approximately).
Step 5: Calculate Alison's time for the race. We know that time = distance/speed. So, Alison's time = 5000 m / 2.17 m/s = 2304 seconds (approximately).
So, Alison's time for the race was approximately 2304 seconds.
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