Quadratic equations and inequalities

1003085405

Level: 
C
Little Red Riding Hood ran (at instantaneous speed) through the forest to see her grandmother, who lives in a cottage, which is \( 4\,\mathrm{km} \) distant. If she ran by \( 4\,\mathrm{km/h} \) faster, she would meet her grandmother \( 10 \) minutes sooner. What was Little Red Riding Hood’s speed?
\( 8\,\mathrm{km/h} \)
\( 12\,\mathrm{km/h} \)
\( 10\,\mathrm{km/h} \)
\( 6\,\mathrm{km/h} \)

1003085408

Level: 
C
A swimming pool can be filled by two pipes in \( 5 \) hours. It takes \( 24 \) hours longer to fill the pool by only the first pipe than by only the second one. In how many hours does the first pipe fill the pool, in how many hours does the second one? Find the sum of both times.
\( 36 \) hours
\( 20 \) hours
\( 18 \) hours
\( 32 \) hours

9000033708

Level: 
C
A stone has been thrown vertically up at the velocity \(15\, \mathrm{m}\, \mathrm{s}^{-1}\) from the initial height \(10\, \mathrm{m}\). How long (in seconds) has been the height of the stone at least \(20\, \mathrm{m}\)? Hint: The height \(h\) is given by the expression \(h = s_{0} + v_{0}t -\frac{1} {2}gt^{2}\), the standard acceleration is \(g\mathop{\mathop{\doteq }}\nolimits 10\, \mathrm{m}\, \mathrm{s}^{-2}\).
exactly \(1\, \mathrm{s}\)
less than \(1\, \mathrm{s}\)
more than \(1\, \mathrm{s}\)
The information is not sufficient to give a definite answer.

9000033709

Level: 
C
A square shaped garden with the side \(a\) should be reduced by a length \(x\) to another square garden. The difference between the areas of the gardens should not be bigger than \(25\%\) of the original area. Find the possible values of \(x\).
\(x\leq a -\frac{\sqrt{3}} {2} a\)
\(x\leq \sqrt{3}a\)
\(x\leq \frac{3} {4}a\)
\(x\leq a + \frac{\sqrt{3}} {2} a\)