Set 6

A coach is training $3$ students. The training involves jogging on a circular track. Jogging starts at $07:00$ from the start line. Below is the record of how long it takes for each runner to return to the start line.

According to the coach's notes, until exactly $09:24$, the three runners have passed the start line together $4$ times.

Then the value of $x$ is ....

A coach is training $3$ students. The training involves jogging on a circular track. Jogging starts at $07:00$ from the start line. Below is the record of how long it takes for each runner to return to the start line.

According to the coach's notes, until exactly $09:24$, the three runners have passed the start line together $4$ times.

If the average speed of runner $A$ is $2$ meters per second, then the length of the track is ....

Babehhh is a financially literate person. He received money from a good person amounting to $\text{Rp}12,500,000.00$. He saved the money in a bank. After one year, his money became $\text{Rp}15,000,000.00$. Thus, the money grew due to interest of ....

Bima saves money in a bank amounting to $\text{Rp}15,000,000.00$ with an interest of $12\%$ per year. After some years, Bima withdraws all his savings amounting to $\text{Rp}16,500,000.00$. Thus, the duration Bima saved his money is ....

Two types of sand, sand A and sand B, are poured separately to form cones. The base radius of sand cone A is always equal to its height, while the base radius of sand cone B is twice its height. $P_1$ is the center of the base of sand pile A and $P_2$ is the center of the base of sand pile B. The distance between $P_1$ and $P_2$ is $10$ m.

If both types of sand are poured at the same volumetric rate, then $R_1 : R_2 = ....$

Two types of sand, sand A and sand B, are poured separately to form cones. The base radius of the sand A cone is always equal to its height, while the base radius of the sand B cone is twice its height. $P_1$ is the center of the base of sand pile A and $P_2$ is the center of the base of sand pile B. The distance between $P_1$ and $P_2$ is $10$ m.

If both types of sand are poured at the same volumetric rate, then $h_1 : h_2 = ....$

An automotive factory produces cars. Each month, the number of cars that can be produced follows an arithmetic sequence. If in January $2024$ it can produce $100$ units, and in April $2024$ it produces $160$ units.

Then the total number of cars that can be produced by the end of the year is ....

A construction worker wants to cut a wooden plank into $6$ pieces. The length of each piece follows a geometric series. If the shortest piece is $3$ cm and the longest is $96$ cm.

Then the total length of the original wooden plank is ....

A telecommunications company provides landline services. The company stipulates that the tariff paid in a regional unit for a month is calculated by multiplying the call duration (in minutes) by the call rate per minute, then adding the monthly subscription fee.

The rate per minute set in region A is Rp$150.00$ more than the call duration (in minutes). The tariff paid by a customer for a month is denoted by $y$, the call duration (in minutes) is denoted by $x$, and the monthly subscription fee is denoted by $z$. The monthly subscription fee is set at Rp$60,000.00$.

Which of the following is the function for the landline tariff paid by a customer for a month?

In forming a committee, a company requires $3$ staff members. They will be placed as chairman, secretary, and treasurer. There are $7$ candidates available.

Then the number of possible staff committee arrangements is ....

A research team is to be formed, consisting of $2$ mathematicians and $3$ physicists. If the available candidates are $3$ mathematicians and $5$ physicists.

Then the number of ways to form the team is ....

Normally, a phone battery can reach $100\%$ charge in $2.5$ hours, from $20\%$ condition. If Babeh's phone battery is currently as shown in the image ($60\%$):

Assuming the same charging power. Then to reach full energy percentage, the time required is ....

A train consists of $8$ train carriages. One carriage has a seating capacity for $25$ passengers. The train passes through $8$ stations.

The transportation management sets a base fare of $\text{Rp}2,500.00$ for the first kilometer. And it increases by $\text{Rp}1,000.00$ for each subsequent $1$ kilometer.

Suppose Bedu wants to travel from the first station to the $5$th station, which is a distance of $18$ km. What is the total fare he has to pay?

Employees in an MSME are divided into three groups.

Group $A$ employees earn a monthly salary equal to one-third of Group $B$ employees, while Group $C$ employees are paid a monthly salary equal to half of Group $B$ employees' salary.

The income of Group $A$ for $6$ months will be equal to the income of Group $C$ employees for ....

To transport $96$ kg of goods simultaneously, a company rents $20$ pickup trucks. The carrying capacity of each truck varies. The carrying capacities of truck types $\text{I}$, $\text{II}$, and $\text{III}$ are $3$, $4$, and $6$ kg, respectively.

If the company rents $4$ type $\text{I}$ trucks, then the number of type $\text{II}$ trucks rented is ....

The average weight of ten futsal players is $60$ kg. One of them is replaced by Iksan, so the average weight becomes $60.5$ kg.

If Iksan weighs $62$ kg, then the weight of the replaced futsal player is ....

The average physics test score of a group of students in a class is $62$. If the average scores of male and female students are $50$ and $70$ respectively, then the ratio of the number of male students to female students is ....

A cube $ABCD.EFGH$ has an edge length of $4$ units. If $\angle \alpha$ is $\angle HDF$, then the value of $\sin \alpha$ is ....

A sniper is aiming at a target from the top of a building. The building has a height of $61.73$ meters. The target is a mafia boss with a height of $173$ cm. If the distance of the target from the base of the building is $180$ meters, then the tangent value of the angle of depression between the horizontal line of sight and the shooting line towards the target so that the shot hits the target's head is....

A coach is training $3$ students. The exercise performed is jogging on a circular track. Jogging starts at $07.00$ from the start line. Below is the record of how long it takes for each runner to return to the start line.

According to the coach's notes, until exactly $09.24$, the three runners have passed the start line together $4$ times.

Given that runner A's speed is $2$ m/s.

$72$ minutes after they started running, the difference in the length of the track covered by runner A and C is ....