c4 solomon paper I question 7a

just been doing this paper and don't understand why
1) its not dx/dt = -kx(1-x) as opposed to positive k because x is decreasing
2) why 1/8=k*1/4*3/4

any help is appreciated, thank you!

1) $x$ is increasing though. It is defined to the be the amount of wheat that is destroyed, so $\frac{dx}{dt}=kx(1-x)$
2) Over 6 hours, the destroyed crops increase. It begins with only $x=\frac{1}{4}$ being destroyed, and end up with all of it being destroyed. So $x=1$. Meaning the rate of change is quite simply $\frac{1-\frac{1}{4}}{6}$ which brings it to $\frac{1}{8}$. Since we know the rate of change is modelled by $\frac{dx}{dt}=kx(1-x)$ this means when x=1/4 is destroyed, we have $\frac{1}{8}=k(\frac{1}{4})(1-\frac{1}{4})$

1) $x$ is increasing though. It is defined to the be the amount of wheat that is destroyed, so $\frac{dx}{dt}=kx(1-x)$
2) Over 6 hours, the destroyed crops increase. It begins with only $x=\frac{1}{4}$ being destroyed, and end up with all of it being destroyed. So $x=1$. Meaning the rate of change is quite simply $\frac{1-\frac{1}{4}}{6}$ over the 6 hours in which this is happening which brings it to $\frac{1}{8}$. Since we know the rate of change is modelled by $\frac{dx}{dt}=kx(1-x)$, and is constant for this period, this means when x=1/4 is destroyed, we have $\frac{1}{8}=k(\frac{1}{4})(1-\frac{1}{4})$

how do you actually work out part a) please? on the mark scheme they divide 3/4 by 6 but not sure where the 6 comes from
thanks

Lol you're gonna get man vexed real soon

its alright i think i got it, just quite a strange question