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Chapter 2: Problem 16

To pass a physical fitness test, Massimo must run \(1000 \mathrm{m}\) at an average rate of \(4.0 \mathrm{m} / \mathrm{s} .\) He runs the first $900 \mathrm{m}\( in \)250 \mathrm{s} .$ Is it possible for Massimo to pass the test? If so, how fast must he run the last 100 m to pass the test? Explain.

Short Answer

Expert verified
Answer: No, Massimo cannot pass the fitness test because he has already spent all of the required 250 seconds running the first 900 meters, leaving him no time to cover the remaining 100 meters.

Step by step solution

01

Calculate Massimo's average speed so far

First, we need to find Massimo's average speed for the first 900 meters he has run. We will use the following formula: average speed = distance (m) / time (s). Massimo has covered 900 meters in 250 seconds. So his average speed for the first 900 meters is: average speed = \(\frac{900}{250}\) = \(3.6 \frac{\mathrm{m}}{\mathrm{s}}\).
02

Calculate the required total time

Massimo must maintain an average speed of 4.0 m/s for the entire 1000-meter run to pass the test. To find the total time required to run 1000 meters at this speed, we can rearrange the formula for the average speed: time (s) = distance (m) / average speed. total time = \(\frac{1000}{4}\) = \(250 \mathrm{s}\).
03

Calculate the remaining time to run 100 meters

Since Massimo has already run the first 900 meters in 250 seconds, we need to calculate how much time he needs to spend running the last 100 meters to maintain the required average speed of 4.0 m/s. Subtract his time for the first 900 meters from the required total time to get the remaining time: remaining time = total time - time spent on 900 meters = 250 - 250 = 0 seconds.
04

Conclusion

Since Massimo has already spent all of the required 250 seconds running the first 900 meters, he has no time left to cover the remaining 100 meters. Therefore, it is not possible for him to pass the test by maintaining an average speed of 4.0 m/s for the entire 1000 meters.

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Most popular questions from this chapter

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