Chapter 9.5, Problem 62E

To determine

To calculate the time after heavy rain.

Answer to Problem 62E

The river is 6 feet deep after 24.04 and 72.12hours of rain.

Explanation of Solution

Given information:

Depth of the river is,

  $d=-0.25t^2+1.7t+3.5$

Where, d is depth

t is time after rain

depth is 6 feet.

Formula used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

For speed, substituting the values,

  $6=-0.25t^2+1.7t+3.5$

Shifting the values,

  $-0.25t^2+1.7t+3.5-6=0$

On solving,

  $-0.25t^2+1.7t-2.5=0$

So,

  $a=-0.25$ ,

  $b=1.7$ and

  $c=-2.5$

Substituting the values,

  $x=\frac{-1.7\pm \sqrt{{(1.7)}^2-4(-0.25)(-2.5)}}{2(-0.25)}$

On solving,

  $x=\frac{-1.7\pm \sqrt{0.39}}{-0.5}$

On solving,

  $x=\frac{-1.25\pm 0.625}{-0.026}$

For +0.625,

  $x=\frac{-1.25+0.625}{-0.026}$

On solving,

  $x=24.04$

For -0.625,

  $x=\frac{-1.25-0.625}{-0.026}$

On solving,

  $x=72.12$

Hence, the river is 6 feet deep after 24.04 and 72.12hours of rain.