Ice is usually used in cool drinks to further cool them - NSC Mathematical Literacy - Question 5 - 2023 - Paper 2

To find the total mass of the ice blocks, we know that each block weighs 2 tons. First, we convert tons to kilograms:

$$1 ext{ ton} = 1,000 ext{ kg} ext{ (or equivalently, } 1 ext{ ton} = 2,000 ext{ kg for accurate conversion calculations)}$$

So, for 60 blocks:

$$ext{Total Mass} = 60 ext{ blocks} imes 2,000 ext{ kg/block} = 120,000 ext{ kg}$$

Therefore, the total mass of the wall is 120,000 kg.

We are given that a block of ice was carved out to make a circular opening, resulting in a volume of 38,500 cm³. We will use the volume formula to determine the volume of the ice that was carved out:

Using the formula for converting volume of ice to volume of water:

$$ext{Volume of Ice} = ext{Volume of water} imes 0.92$$

Substituting the known volume:

$$ext{Volume of Ice} = 38,500 ext{ cm}^3 imes 0.92 = 35,420 ext{ cm}^3$$

Thus, the volume of the ice that was carved out is 35,420 cm³.

The distances given are:

• From Washington to Anchorage: 3,350 nautical miles.
• From Tokyo to Honolulu: 2,607 nautical miles.

To find the difference:

$$ext{Difference} = 3,350 - 2,607 = 743 ext{ nautical miles}$$

Therefore, the difference in distance is 743 nautical miles.

From the previous information, we have:

$$1 ext{ nautical mile} = 1,151 ext{ miles} ext{ and } 1 ext{ km} = 0.6215 ext{ miles}$$

First, we will convert the nautical miles to miles:

$$ext{Distance in miles} = 950 ext{ nautical miles} imes 1,151 ext{ miles/nautical mile} = 1,095,450 ext{ miles}$$

Then convert this distance to kilometers:

$$ext{Distance in km} = ext{Distance in miles} imes 0.6215 = ext{Distance in miles} imes 1,60934.$$

The distance from Berlin to Anchorage is 1,771 km approximately.

From the previous calculations, we have:

• The distance from LA to Honolulu is 2,607 nautical miles.
• The average speed of the ship is approximately 10.68 nautical miles/hour.
• The time to sail from LA to Honolulu is:

ext{Time} = rac{2,607 ext{ nm}}{10.68 ext{ nm/hr}} ext{ hours} = 243 ext{ hours}

Adding the travel time to the departure: Departure: September 24, 16:00.

Add 243 hours (or 10 days and 3 hours) for the first leg:

Arrival in Honolulu: October 5, 19:00.

Then for the second leg: Distance from Honolulu to Tokyo is 3,350 nautical miles:

ext{Time} = rac{3,350 ext{ nm}}{10.68 ext{ nm/hr}} ext{ hours} = 313.67 ext{ hours}

Add this to the arrival time in Honolulu:

From October 5, 19:00 add 313.67 hours (approximately 13 days):

Final arrival time in Tokyo: October 18, 16:40.