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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 20092009 , Usain Bolt set the world record for sprinting approximately 935 9 \frac{3}{5} seconds.\newlineFind his average speed in meters per second.\newline□\square meters per second

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Q. In 20092009 , Usain Bolt set the world record for sprinting approximately 935 9 \frac{3}{5} seconds.\newlineFind his average speed in meters per second.\newline□\square meters per second
  1. Convert to Improper Fraction: Convert the time taken to sprint 100100m into an improper fraction.\newlineUsain Bolt's world record time is given as 9(35)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.\newline9×5+3=45+3=489 \times 5 + 3 = 45 + 3 = 48\newlineSo, 9(35)9\left(\frac{3}{5}\right) seconds is equivalent to 485\frac{48}{5} seconds.
  2. Calculate Average Speed: Calculate the average speed using the formula speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}. The distance covered is 100100 meters, and the time taken is 485\frac{48}{5} seconds. The average speed is therefore: Speed=DistanceTime=100 meters(485 seconds)\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{100 \text{ meters}}{\left(\frac{48}{5} \text{ seconds}\right)}
  3. Perform Division: Perform the division to find the average speed.\newlineTo divide by a fraction, multiply by its reciprocal. So, we multiply 100100 meters by the reciprocal of 485\frac{48}{5} seconds, which is 548\frac{5}{48}.\newlineSpeed = 100100 meters ×(548)\times \left(\frac{5}{48}\right) seconds
  4. Simplify Expression: Simplify the expression to find the average speed. Speed = (100×5)/48(100 \times 5) / 48 meters per second = 500/48500 / 48 meters per second
  5. Reduce Fraction: Reduce the fraction to its simplest form. \newline50048\frac{500}{48} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 44.\newlineSpeed = (500/4)(48/4)\frac{(500 / 4)}{(48 / 4)} meters per second = 12512\frac{125}{12} meters per second
  6. Convert to Mixed Number: Convert the improper fraction to a mixed number if necessary.\newlineHowever, 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.\newlineSpeed = 12512\frac{125}{12} meters per second ≈10.4167\approx 10.4167 meters per second

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