Question

A flare is fired straight up from a ship at sea. Solve the equation $16(t^2-13t+40)=0$ for t, the number of seconds it will take for the flare to be at an altitude of 640 feet.

Short answer

t = 0 and t = 13 .

Step-by-step solution

Step 1. Given equation 

$16(t^2-13t+40)=0$, Altitude = 640 feet .

Step 2. Solving 

Given equation is ,

$$\begin{gathered} 16(t^2-13t+40)=0 \\ \mathrm{Now}, \\ 16(t^2-13t+40)=640 \\ {t}^2-13t+40=40 \\ t(t-13)=0 \end{gathered}$$

Therefore , t = 0 and t = 13 are two possible value .

Step 3. Checking 

$$\begin{gathered} \mathrm{At}t=0,16({\left(0\right)}^2-13(0)+40)=16\left(40\right)=640 \\ \mathrm{At}t=13,16(\hspace{0.17em}{\left(13\right)}^2-13(13)+40)=640 \end{gathered}$$

Therefore , 0 and 13 are satisfying the value .