Linear Equations and Inequalities

1003197402

Level: 
C
Paul rides the bike at a constant speed of \( 18\,\mathrm{kph} \). Eighteen minutes after Paul starts his trip, Tom takes the same route on a motorbike at an average speed of \( 40\,\mathrm{kph} \). How far behind Paul will Tom be after \( 12 \) minutes of his ride?
\( 1\,\mathrm{km} \)
\( 60\,\mathrm{km} \)
\( 14\,\mathrm{km} \)
after \( 12 \) minutes of ride Tom will be in front of Paul

1003197403

Level: 
C
An express train of length \( 150\,\mathrm{m} \) travels at the constant speed of \( 144\,\mathrm{kph} \). On a parallel track in the opposite direction travels a freight train of length \( 240\,\mathrm{m} \) at the constant speed of \( 90\,\mathrm{kph} \). How long does it take for trains to pass each other?
\( 6\,\mathrm{s} \)
\( 1.\overline{6}\,\mathrm{s} \)
\( 7.\overline{2} \)
\( 26\,\mathrm{s} \)

1003197404

Level: 
C
The stock of the monitored company lost \( 12\,\% \) of its value during a week. Its fall continued over the next week, and the value declined by another \( 4\,\% \). Let’s denote the original value of the stock by an \( x \). From the following possibilities, choose the expression that gives the value of the stock at the end of the monitored term.
\( 0.96\cdot0.88x \)
\( (0.96+0.88)x \)
\( 0.04\cdot0.12x \)
\( [1-(0.04+0.12)]x \)

1003197405

Level: 
C
Nine people travel by bus. The same number of people gets off the bus at each of three bus stops and then so many people get in to double the number of remaining bus passengers. After the third bus stop there are \( 30 \) people in the bus. How many passengers get off at each bus stop?
\( 3 \)
\( 2 \)
\( 1 \)
\( 6 \)

1003197406

Level: 
C
Each of two companies should deliver the same amount of raw material. While inspecting it was found out that the company \( A \) delivered \( 150\,\mathrm{kg} \) and the company \( B \) delivered \( 194\,\mathrm{kg} \). At the moment of inspection, company \( A \) has to deliver yet three times more than what is left to be delivered by company \( B \). Choose the equation which does NOT correspond to the described situation.
\( 3(x-150)=x-194 \), where \( x \) represents the total planned delivery of both companies.
\( x-150=3(x-194) \), where \( x \) represents the total planned delivery of both companies.
\( 150+3x=194+x \), where \( x \) represents the amount of raw material which is left to be delivered by company \( B \).
\( 150+x=194+\frac x3 \), where \( x \) represents the amount of raw material which is left to be delivered by company \( A \).

1003197407

Level: 
C
A hose can fill the garden pool in \( 20 \) hours. The owners bought a pump that guarantees filling the pool in \( 8 \) hours. However, a crack appeared in the pool's shell which can drain all the water from the full pool within \( 5 \) days. How long will it take to fill the pool with the hose and the pump at the same time as the water runs off through the crack?
exactly \( 6 \) hours
approximately \( 5.7 \) hours
approximately \( 5.5 \) hours
approximately \( 6.8 \) hours

1003197408

Level: 
C
The painter \( A \) takes \( 15 \) hours to paint a flat. The painter \( B \) takes \( 12 \) hours to paint the same flat and the painter \( C \) takes \( 10 \) hours to complete the same task. The painter \( A \) starts to paint alone and after \( 2 \) hours joins him the painter \( B \). After the next hour the painter \( C \) starts to paint with them too. How long will all three painters paint together before completing the work?
\( 2\,\mathrm{h}\ 52\,\mathrm{min} \)
\( 3\,\mathrm{h}\ 8\,\mathrm{min} \)
\( 3\,\mathrm{h}\ 24\,\mathrm{min} \)
\( 4\,\mathrm{h} \)

2010011202

Level: 
C
Students registered for sports camps. For the biking camp registered by \( 12 \) students more than for the boating camp. After some time one of the students switched his registration from the boating camp to the biking camp. Now, there is three times more bikers than boaters. How many students registered originally for the biking camp?
\( 20 \)
\( 21 \)
\( 7 \)
\( 8 \)