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In 2009, Usain Bolt set the world record for sprinting 100m in approximately 9(3)/(5) seconds.
Find his average speed in meters per second.
◻ meters per second

In $2009$ , Usain Bolt set the world record for sprinting approximately $9 \frac{3}{5}$ seconds. $\newline$ Find his average speed in meters per second. $\newline$ $\square$ meters per second

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Interpret measures of center and variability

Full solution

Q. In

2009

, Usain Bolt set the world record for sprinting approximately

9 \frac{3}{5}

seconds.

\newline

Find his average speed in meters per second.

\newline

\square

meters per second

Convert to Improper Fraction: Convert the time taken to sprint $100$ m into an improper fraction. $\newline$ Usain Bolt's world record time is given as $9\left(\frac{3}{5}\right)$ seconds. To convert this mixed number into an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. $\newline$ $9 \times 5 + 3 = 45 + 3 = 48$ $\newline$ So, $9\left(\frac{3}{5}\right)$ seconds is equivalent to $\frac{48}{5}$ seconds.
Calculate Average Speed: Calculate the average speed using the formula $\text{speed} = \frac{\text{distance}}{\text{time}}$ . The distance covered is $100$ meters, and the time taken is $\frac{48}{5}$ seconds. The average speed is therefore: $\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{100 \text{ meters}}{\left(\frac{48}{5} \text{ seconds}\right)}$
Perform Division: Perform the division to find the average speed. $\newline$ To divide by a fraction, multiply by its reciprocal. So, we multiply $100$ meters by the reciprocal of $\frac{48}{5}$ seconds, which is $\frac{5}{48}$ . $\newline$ Speed = $100$ meters $\times \left(\frac{5}{48}\right)$ seconds
Simplify Expression: Simplify the expression to find the average speed. Speed = $(100 \times 5) / 48$ meters per second = $500 / 48$ meters per second
Reduce Fraction: Reduce the fraction to its simplest form. $\newline$ $\frac{500}{48}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $4$ . $\newline$ Speed = $\frac{(500 / 4)}{(48 / 4)}$ meters per second = $\frac{125}{12}$ meters per second
Convert to Mixed Number: Convert the improper fraction to a mixed number if necessary. $\newline$ However, since we are looking for the speed in meters per second, we can leave the answer as an improper fraction or convert it to a decimal. $\newline$ Speed = $\frac{125}{12}$ meters per second $\approx 10.4167$ meters per second

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