Sure, let's go through each question step-by-step.
### Question 4
Question: Thandi runs [tex]\(126.65 \, \text{km}\)[/tex] further than Lindiwe. If Thandi runs [tex]\(260.42 \, \text{km}\)[/tex] altogether, how far does Lindiwe run?
Step-by-Step Solution:
1. Identify the total distance run by Thandi.
[tex]\[ \text{Thandi's total distance} = 260.42 \, \text{km} \][/tex]
2. Identify how much further Thandi runs compared to Lindiwe.
[tex]\[ \text{Distance difference} = 126.65 \, \text{km} \][/tex]
3. Calculate Lindiwe's running distance by subtracting the distance difference from Thandi's total distance.
[tex]\[ \text{Lindiwe's distance} = \text{Thandi's total distance} - \text{Distance difference} \][/tex]
[tex]\[ \text{Lindiwe's distance} = 260.42 \, \text{km} - 126.65 \, \text{km} \][/tex]
[tex]\[ \text{Lindiwe's distance} = 133.77 \, \text{km} \][/tex]
So, Lindiwe runs [tex]\(133.77 \, \text{km}\)[/tex].
### Question 5
Mum cut off [tex]\(\frac{2}{5}\)[/tex] of a 40 cm ribbon.
Part a: What length was cut off?
Step-by-Step Solution:
1. Identify the total length of the ribbon.
[tex]\[ \text{Total ribbon length} = 40 \, \text{cm} \][/tex]
2. Identify the fraction of the ribbon that was cut off.
[tex]\[ \text{Fraction cut off} = \frac{2}{5} \][/tex]
3. Calculate the length cut off by multiplying the total ribbon length by the fraction cut off.
[tex]\[ \text{Length cut off} = \text{Total ribbon length} \times \text{Fraction cut off} \][/tex]
[tex]\[ \text{Length cut off} = 40 \, \text{cm} \times \frac{2}{5} \][/tex]
[tex]\[ \text{Length cut off} = 16 \, \text{cm} \][/tex]
So, the length cut off was [tex]\(16 \, \text{cm}\)[/tex].
Part b: What length was left?
Step-by-Step Solution:
1. Identify the total length of the ribbon.
[tex]\[ \text{Total ribbon length} = 40 \, \text{cm} \][/tex]
2. Identify the length that was cut off.
[tex]\[ \text{Length cut off} = 16 \, \text{cm} \][/tex]
3. Calculate the length that was left by subtracting the length cut off from the total ribbon length.
[tex]\[ \text{Length left} = \text{Total ribbon length} - \text{Length cut off} \][/tex]
[tex]\[ \text{Length left} = 40 \, \text{cm} - 16 \, \text{cm} \][/tex]
[tex]\[ \text{Length left} = 24 \, \text{cm} \][/tex]
So, the length left was [tex]\(24 \, \text{cm}\)[/tex].
