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SOFTBALL  Chloe pitches at a top speed 3 feet per second faster than Becky. If Chloe’s top speed is x feet per second, which expression represents how much longer it takes for ball to travel the 43 feet to the plate when Becky pitches?

Question

SOFTBALL  Chloe pitches at a top speed 3 feet per second faster than Becky. If Chloe’s top speed is x feet per second, which expression represents how much longer it takes for ball to travel the 43 feet to the plate when Becky pitches?

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Solution

Let's break down the problem step by step.

  1. Identify the given information:

    • Chloe's top speed is x x feet per second.
    • Chloe pitches 3 feet per second faster than Becky.
  2. Determine Becky's top speed:

    • Since Chloe pitches 3 feet per second faster than Becky, Becky's top speed is x3 x - 3 feet per second.
  3. Calculate the time it takes for Chloe's pitch to travel 43 feet:

    • Time is calculated by dividing the distance by the speed.
    • For Chloe: TimeChloe=43 feetx feet per second \text{Time}_{\text{Chloe}} = \frac{43 \text{ feet}}{x \text{ feet per second}} .
  4. Calculate the time it takes for Becky's pitch to travel 43 feet:

    • For Becky: TimeBecky=43 feet(x3) feet per second \text{Time}_{\text{Becky}} = \frac{43 \text{ feet}}{(x - 3) \text{ feet per second}} .
  5. Determine the difference in time:

    • The difference in time is TimeBeckyTimeChloe \text{Time}_{\text{Becky}} - \text{Time}_{\text{Chloe}} .
    • Substitute the expressions for time: Difference in time=43x343x \text{Difference in time} = \frac{43}{x - 3} - \frac{43}{x}

So, the expression that represents how much longer it takes for the ball to travel the 43 feet to the plate when Becky pitches is: 43x343x \frac{43}{x - 3} - \frac{43}{x}

This problem has been solved

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