Answer:
319 seconds
Step-by-step explanation:
The distance 12.42 miles is equivalent to
12.42*5280=65577.6 ft
[tex]ma-mgsin\theta=ma_{net} [/tex]
When slope is 6.4%, [tex]\theta=tan^{-1} 0.064=3.67^{\circ} [/tex]
[tex]a_{net}=a-gsin\theta=2.93-32.2sin3.67=-0.87 [/tex]
Therefore, [tex]a_{net}=-0.87 ft/s^{2} [/tex]
Also
[tex]s=ut+0.5a_{net} [/tex]
[tex]65577.6=297.73t+0.5(-0.87)t^{2} [/tex]
[tex]0.87t^{2}-297.73t+6577.6=0 [/tex]
Making t the subject of the formula by solving quadratic equation
t=318.4791278210496
Therefore, time is 319 seconds
