Question

Your cousin was standing along a parade was traveling route when she spotted a float 750 ft from her. the parade was traveling at 158ft/min. the distance d from your cousin in feet after t minutes is given by d = |750-158ft|. At what times is the float 200ft from your cousin? Round to the nearest tenth.

Answer 1

To find the times the float is 200ft from your cousin, solve the absolute value equation d = |750 - 158t| by setting d to 200 ft and t ≈ 3.5 minutes after rounding to the nearest tenth.

Step-by-step explanation:

To determine at what times the float is 200ft from your cousin, we need to solve for when the distance d equals 200 ft. The distance d from your cousin in feet after t minutes is given by d = |750 - 158t|. We set this equal to 200 ft to find the times:

1. Absolute value equations often have two solutions because the expression inside the absolute value can be both positive and negative. Therefore, we solve for both scenarios:

   • 750 - 158t = 200 for when the float is getting closer to the cousin
   • 750 - 158t = -200 for when the float is moving away from the cousin (if applicable)

2. For the first equation:

   158t = 750 - 200

   t = 550 / 158

   t ≈ 3.5 minutes (after rounding to the nearest tenth)

3. It is important to note that the second equation:

   750 - 158t = -200 does not make physical sense in this context as it would imply the float having moved past the initial position of your cousin, and given the scenario, we are only considering the approach of the float to the cousin. So we only consider the time for the float moving towards your cousin.

The float will therefore be 200 ft from your cousin at t ≈ 3.5 minutes.