Each group gets to use the new playground for 90 minutes during school fun day. If your class uses the…

Question

Each group gets to use the new playground for 90 minutes during school fun day. If your class uses the playground for 1/3 of the total play sessions and there are 21 sessions in total, how many minutes does your class spend on the playground?

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Here are the solutions to the problems:

: Playground usage

Determine the total time available for the playground.
The playground is available for 90 minutes in total.
Calculate the number of sessions your class uses.
Your class uses $\frac{1}{3}$ of the total 21 sessions.
$\text{Class sessions} = \frac{1}{3} \times 21 = 7 \text{ sessions}$
Calculate the duration of each session.
The total time (90 minutes) is divided among 21 sessions.
$\text{Duration per session} = \frac{90 \text{ minutes}}{21 \text{ sessions}}$
Calculate the total time your class spends on the playground.
Multiply the number of sessions your class uses by the duration of each session.
$\text{Total time for class} = 7 \text{ sessions} \times \frac{90 \text{ minutes}}{21 \text{ sessions}}$ $\text{Total time for class} = \frac{630}{21} \text{ minutes}$ $\text{Total time for class} = 30 \text{ minutes}$
Your class spends $\boxed{\text{30 minutes}}$ on the playground.

: Temperature drop
Note the initial temperature.
Initial temperature at 8 AM = $12^\circ\text{C}$ .
Calculate the temperature at 12 PM.
The temperature drops by $4^\circ\text{C}$ by 12 PM.
$\text{Temperature at 12 PM} = 12^\circ\text{C} - 4^\circ\text{C}$ $\text{Temperature at 12 PM} = 8^\circ\text{C}$
Calculate the temperature at 6 PM.
The temperature drops another $9^\circ\text{C}$ by 6 PM.
$\text{Temperature at 6 PM} = 8^\circ\text{C} - 9^\circ\text{C}$ $\text{Temperature at 6 PM} = -1^\circ\text{C}$
The temperature at 6 PM is $\boxed{\text{-1}^\circ\text{C}}$ .

: Tyre ratio
Determine the total number of parts in the ratio.
The ratio for tyre swings, balancing beams, and climbing walls is 3:2:1.
$\text{Total parts} = 3 + 2 + 1 = 6$
Calculate the value of one part.
There are 60 tyres in total.
$\text{Value of one part} = \frac{60 \text{ tyres}}{6 \text{ parts}}$ $\text{Value of one part} = 10 \text{ tyres/part}$
Calculate the number of tyres used for tyre swings.
Tyre swings correspond to 3 parts of the ratio.
$\text{Tyres for swings} = 3 \times 10 \text{ tyres/part}$ $\text{Tyres for swings} = 30 \text{ tyres}$
The number of tyres used for the tyre swings is $\boxed{\text{30 tyres}}$ .

Each group gets to use the new playground for 90 minutes during school fun day. If your class uses the playground for 1/3 of the total play sessions and there are 21 sessions in total, how many minutes does your class spend on the playground?

Step-by-step solution

Determine the total time available for the playground.

Calculate the number of sessions your class uses.

Calculate the duration of each session.

Calculate the total time your class spends on the playground.

Note the initial temperature.

Calculate the temperature at 12 PM.

Calculate the temperature at 6 PM.

Determine the total number of parts in the ratio.

Calculate the value of one part.

Calculate the number of tyres used for tyre swings.

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