Question

23 wayde van niekerk, a runner from south africa, ran 400 meters in 43.03 seconds to set a world record. which calculation would determine his average speed, in miles per hour?

1. \\(\frac{400,\text{m}}{43.03,\text{sec}} cdot \frac{1000,\text{m}}{0.62,\text{mi}} cdot \frac{1,\text{hr}}{3600,\text{sec}}\\)
2. \\(\frac{400,\text{m}}{43.03,\text{sec}} cdot \frac{0.62,\text{mi}}{1000,\text{m}} cdot \frac{1,\text{hr}}{3600,\text{sec}}\\)
3. \\(\frac{400,\text{m}}{43.03,\text{sec}} cdot \frac{0.62,\text{mi}}{1000,\text{m}} cdot \frac{3600,\text{sec}}{1,\text{hr}}\\)
4. \\(\frac{400,\text{m}}{43.03,\text{sec}} cdot \frac{1000,\text{m}}{0.62,\text{mi}} cdot \frac{3600,\text{sec}}{1,\text{hr}}\\)

problem 14
25 elenas fastest time for the 50 - meter dash is 7 seconds. she wants to know how fast this is in inches per minute. which expression can elena use for a correct conversion?

1. \\(\frac{7,\text{sec}}{50,\text{meters}} cdot \frac{60,\text{sec}}{1,\text{min}} cdot \frac{1,\text{meter}}{39.37,\text{in}}\\)
2. \\(\frac{7,\text{sec}}{50,\text{meters}} cdot \frac{1,\text{min}}{60,\text{sec}} cdot \frac{39.37,\text{in}}{1,\text{meter}}\\)
3. \\(\frac{50,\text{meters}}{7,\text{sec}} cdot \frac{60,\text{sec}}{1,\text{min}} cdot \frac{1,\text{meter}}{39.37,\text{in}}\\)
4. \\(\frac{50,\text{meters}}{7,\text{sec}} cdot \frac{60,\text{sec}}{1,\text{min}} cdot \frac{39.37,\text{in}}{1,\text{meter}}\\)

problem 15
27 in 2009, usain bolt, a sprinter from jamaica, set the world record in the 100 - meter dash with a time of 9.58 seconds. his approximate speed, in kilometers per hour, can be found using which conversion?

1. \\(\frac{9.58,\text{sec}}{100,\text{m}} cdot \frac{1000,\text{m}}{1,\text{km}} cdot \frac{1,\text{min}}{60,\text{sec}} cdot \frac{1,\text{hr}}{60,\text{min}}\\)
2. \\(\frac{100,\text{m}}{9.58,\text{sec}} cdot \frac{60,\text{sec}}{1,\text{min}} cdot \frac{1000,\text{m}}{1,\text{km}} cdot \frac{60,\text{min}}{1,\text{hr}}\\)
3. \\(\frac{100,\text{m}}{9.58,\text{sec}} cdot \frac{1,\text{km}}{1000,\text{m}} cdot \frac{1,\text{min}}{60,\text{sec}} cdot \frac{1,\text{hr}}{60,\text{min}}\\)
4. \\(\frac{100,\text{m}}{9.58,\text{sec}} cdot \frac{60,\text{sec}}{1,\text{min}} cdot \frac{1,\text{km}}{1000,\text{m}} cdot \frac{60,\text{min}}{1,\text{hr}}\\)

Explanation:

Problem 23

Step1: Start with base speed

$\frac{400\ \text{m}}{43.03\ \text{sec}}$

Step2: Convert meters to miles

$\frac{400\ \text{m}}{43.03\ \text{sec}} \times \frac{0.62\ \text{mi}}{1000\ \text{m}}$

Step3: Convert seconds to hours

$\frac{400\ \text{m}}{43.03\ \text{sec}} \times \frac{0.62\ \text{mi}}{1000\ \text{m}} \times \frac{3600\ \text{sec}}{1\ \text{hr}}$

Step1: Start with base speed

$\frac{50\ \text{meters}}{7\ \text{sec}}$

Step2: Convert seconds to minutes

$\frac{50\ \text{meters}}{7\ \text{sec}} \times \frac{60\ \text{sec}}{1\ \text{min}}$

Step3: Convert meters to inches

$\frac{50\ \text{meters}}{7\ \text{sec}} \times \frac{60\ \text{sec}}{1\ \text{min}} \times \frac{39.37\ \text{in}}{1\ \text{meter}}$

Step1: Start with base speed

$\frac{100\ \text{m}}{9.58\ \text{sec}}$

Step2: Convert seconds to minutes

$\frac{100\ \text{m}}{9.58\ \text{sec}} \times \frac{60\ \text{sec}}{1\ \text{min}}$

Step3: Convert meters to km

$\frac{100\ \text{m}}{9.58\ \text{sec}} \times \frac{60\ \text{sec}}{1\ \text{min}} \times \frac{1\ \text{km}}{1000\ \text{m}}$

Step4: Convert minutes to hours

$\frac{100\ \text{m}}{9.58\ \text{sec}} \times \frac{60\ \text{sec}}{1\ \text{min}} \times \frac{1\ \text{km}}{1000\ \text{m}} \times \frac{60\ \text{min}}{1\ \text{hr}}$

Answer:

1. $\frac{400\ \text{m}}{43.03\ \text{sec}} \cdot \frac{0.62\ \text{mi}}{1000\ \text{m}} \cdot \frac{3600\ \text{sec}}{1\ \text{hr}}$

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Problem 25