Linear equations and inequalities

1003029706

Level: 
C
In a river, water flows at speed of \( 1\,\mathrm{mps} \). A boat, which moves at speed of \( 4\,\mathrm{mps} \) in a calm water, carries mail to a little town distant \( 6\,\mathrm{km} \) downstream. How long will it take till the boat returns? (We disregard the time necessary for mail-handover.) Note: Abbreviation "mps" stands for meter per second.
\( 53\,\mathrm{min}\ 20\,\mathrm{s} \)
\( 50\,\mathrm{min} \)
\( 3\,\mathrm{min}\ 12\,\mathrm{s} \)
\( 1\,\mathrm{min}\ 20\,\mathrm{s} \)

1003031101

Level: 
C
So far Johnny has received the grades: \( 5 \), \( 3 \), \( 3 \), \( 3 \), \( 2 \), \( 2 \), \( 1 \), \( 1 \), for the math course in this school term. What another grade he needs to get so that the average of grades is lower than \( 2.5 \)? (Assumption: All grades are of the same weight in grading scale of \( 1 \), \( 2 \), \( 3 \), \( 4 \), \( 5 \), where \( 1 \) is the best result.)
at worst \( 2 \)
at worst \( 3 \)
only \( 1 \)
The arithmetic mean can’t be less than \( 2.5 \) in any case.

1003031103

Level: 
C
Five litres of a quality wine in by yourself provided bottles cost more than three and a half litres of the same wine in a bigger wine container. The container price is \( 150\,\mathrm{CZK} \). Complete the next statement so that it is true. The price of one litre of this quality wine is
greater than \( 100\,\mathrm{CZK} \).
less than \( 100\,\mathrm{CZK} \).
greater than \( 350\,\mathrm{CZK} \).
greater than \( 500\,\mathrm{CZK} \).

1003031104

Level: 
C
Dan and Jane took a bike trip. Dan rode for \( 3 \) hours at constant speed. Jane rode for half an hour longer at the speed of \( 4\,\mathrm{kph} \) less than Dan’s speed. Identify, which of the following statements about Dan’s speed is true.
The speed is less than \( 28\,\mathrm{kph} \).
The speed is greater than \( 28\,\mathrm{kph} \).
The speed is less than \( 20\,\mathrm{kph} \).
The speed is greater than \( 24\,\mathrm{kph} \).

1003197401

Level: 
C
A man on a bike rides to a distant city at an average speed of \( 24\,\mathrm{kph} \). He will end the trip \( 12 \) minutes earlier, if he increases his average speed by \( 1\,\mathrm{kph} \). How distant is the city?
\( 120\,\mathrm{km} \)
\( 115.2\,\mathrm{km} \)
\( 300\,\mathrm{km} \)
\( 125\,\mathrm{km} \)

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 \( A \).