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1.2 Write the ratio [tex]26:91[/tex] in its simplest form.

1.3 How many minutes are there in [tex]\frac{10^3}{4}[/tex] days?
*Hint: 1 hour [tex]= 60[/tex] minutes, 1 day [tex]= 24[/tex] hours*

1.4 Convert 27.08 km to cm.
*Hint: [tex]1 \text{ km} = 100,000 \text{ cm}[/tex]*

1.5 The scale of a map is [tex]1:500,000[/tex]. If the distance between two points on the map is 37 cm, calculate the actual distance in kilometers.

1.6 Miss Ngomane travels from Tzaneen to Durban. She left Tzaneen at 08:22 and arrived in Cape Town at 06:53 the following day. How long was her journey in hours and minutes?

Answer :

Sure, let's tackle each part of the question step by step.

1.2 Simplify the ratio [tex]\(26:91\)[/tex]:

To simplify a ratio, we need to find the greatest common divisor (GCD) of the numbers. The GCD of 26 and 91 is 13. We divide both numbers by 13:

[tex]\[
\frac{26}{13} : \frac{91}{13} = 2 : 7
\][/tex]

Thus, the ratio in its simplest form is [tex]\(2:7\)[/tex].

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1.3 Calculate the number of minutes in [tex]\(\frac{10^3}{4}\)[/tex] days:

First, calculate [tex]\(\frac{10^3}{4}\)[/tex]:

[tex]\[
\frac{10^3}{4} = \frac{1000}{4} = 250
\][/tex]

Now, calculate the number of minutes in 250 days. We know there are 24 hours in a day and 60 minutes in an hour:

[tex]\[
250 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} = 360,000 \text{ minutes}
\][/tex]

So, there are 360,000 minutes in [tex]\(\frac{10^3}{4}\)[/tex] days.

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1.4 Convert 27.08 km to cm:

To convert kilometers to centimeters, we multiply by 100,000 (because 1 km = 100,000 cm):

[tex]\[
27.08 \text{ km} \times 100,000 = 2,708,000 \text{ cm}
\][/tex]

Therefore, 27.08 km is [tex]\(2,708,000\)[/tex] cm.

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1.5 Calculate the actual distance in kilometers given the map scale:

The scale is 1:500,000, which means 1 cm on the map represents 500,000 cm in reality. If the distance on the map is 37 cm, the real distance is:

[tex]\[
37 \text{ cm} \times 500,000 = 18,500,000 \text{ cm}
\][/tex]

To convert this to kilometers, divide by 100,000:

[tex]\[
18,500,000 \text{ cm} \div 100,000 = 185 \text{ km}
\][/tex]

So, the actual distance is 185 kilometers.

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1.6 Calculate the journey time from Tzaneen to Durban:

The journey starts at 08:22 and ends at 06:53 the following day. To find the duration:

- Calculate time from 08:22 to midnight (00:00),
- Then add the time from midnight to 06:53.

From 08:22 to midnight is 15 hours and 38 minutes (since 24:00 - 08:22 = 15:38).

From midnight to 06:53 is 6 hours and 53 minutes.

Now, add these durations:

15 hours 38 minutes + 6 hours 53 minutes = 22 hours 31 minutes

Therefore, the journey lasted 22 hours and 31 minutes.

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