Question

Bill and Jerry are both taking their hot-air balloons to the balloon show.

Answer 1

9514 1404 393

Answer:

  62.6 seconds

Step-by-step explanation:

We can use the 2-point form of the equation for a line to write equations for the heights of the balloons.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

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For Bill's balloon, the two given points are ...

  (t, h) = (-5, 1032) and (5, 985)

Then the equation is ...

  h = (985 -1032)/(5 -(-5))(t -(-5)) +1032

  h = -47/10(t +5) +1032

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For Jerry's balloon, the two given points are ...

  (t, h) = (0, 0) and (5, 57)

Then the equation is ...

  h = (57-0)/(5-0)(t -0) +0

  h = (57/5)t

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The heights are equal when ...

  -47/10(t +5) +1032 = (57/5)t

  1008.5 = t(57/5 +47/10) = 16.1t

Then the time until heights are the same is ...

  t = 1008.5/16.1 ≈ 62.6 . . . seconds