Question

A truck's distance from a warehouse, d , (measured in miles) is modeled by the formula d = t 2 + 70 t where t represents the number of hours since the truck left the warehouse. The truck's destination is 429.75 miles away. How many hours will it take the truck to reach its destination?

Answer 1

Answer:5.67 h

Step-by-step explanation:

Given

Distance is given by

$d=t^2+70 t$  , t is in hours

Truck destination is 429.75 miles away

i.e. substitute $d=429.75 miles$

$t^2+70t-429.75=0$

Roots of Quadratic Equation can be found  out by

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using this

$t=\frac{-70\pm \sqrt{70^2+4\times 1\times 429.75}}{2\times 1}$

$t=\frac{-70\pm \sqrt{6619}}{2}$

$t=\frac{-70\pm 81.357}{2}$

$t=5.67 hr$

Neglecting negative t