Ski area preparation

A winter ski area is to be prepared by five snow groomers in 6 days. Due to great interest from skiers, after two days reinforcement was called in the form of another three equally performing snow groomers.
Decide for each of the following statements whether it is true, or not.
a) The total time for the area preparation was thanks to the reinforcement shortened to 4.5 days.
b) The total time for the area preparation was thanks to the reinforcement shortened by 25% of the original time.
c) Ten snow groomers would have prepared the area in 2.5 days.

Result

a=

Yes

No

b=

Yes

No

c=

Yes

No

Step-by-step explanation:

$$\begin{gathered} \frac{5}{6}\cdot 2+\frac{3+5}{6}\cdot (x-2)=1 \\ 5/6\cdot 2+(3+5)/6\cdot (x-2)=1 \\ 8x=12 \\ x=\frac{12}{8}=1.5 \\ x=\frac{3}{2}=1.5 \\ x=4.5 \\ a=1 \end{gathered}$$

$$\begin{gathered} p=100\cdot \frac{6-x}{6}=100\cdot \frac{6-1.5}{6}=75\% \\ b=1 \end{gathered}$$

$$\begin{gathered} c_1=5/10\cdot 6=3\text{d} \\ c=0 \end{gathered}$$

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