Certainly! Let's solve the problem step by step.
### Part (i) What is the distance from Akosua's village to Quamu?
1. Calculate the distance Akosua walked:
Akosua's walking rate is [tex]\(1 \frac{1}{2} \text{ km per hour}\)[/tex], which converts to [tex]\(1.5 \text{ km per hour}\)[/tex].
The time she walked is given as 3 hours.
Using the formula:
[tex]\[
\text{Distance} = \text{Rate} \times \text{Time}
\][/tex]
we get:
[tex]\[
\text{Walking Distance} = 1.5 \text{ km per hour} \times 3 \text{ hours} = 4.5 \text{ km}
\][/tex]
2. Calculate the distance the bus traveled:
The bus rate is [tex]\(15 \frac{1}{2} \text{ km per hour}\)[/tex], which converts to [tex]\(15.5 \text{ km per hour}\)[/tex].
The time the bus traveled is given as 2 hours.
Using the same distance formula, we get:
[tex]\[
\text{Bus Distance} = 15.5 \text{ km per hour} \times 2 \text{ hours} = 31 \text{ km}
\][/tex]
3. Calculate the total distance from Akosua's village to Quamu:
The total distance is the sum of the distances Akosua walked and the distance the bus traveled.
[tex]\[
\text{Total Distance} = \text{Walking Distance} + \text{Bus Distance} = 4.5 \text{ km} + 31 \text{ km} = 35.5 \text{ km}
\][/tex]
So, the distance from Akosua's village to Quamu is 35.5 km.
### Part (ii) How long would it take a man, riding a bicycle at 5 km per hour, to travel from Akosua's village to Quamu?
1. Calculate the time to travel the total distance by bicycle:
The rate of the bicycle is 5 km per hour.
We already calculated the total distance to be 35.5 km.
Using the formula:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}}
\][/tex]
we get:
[tex]\[
\text{Cycling Time} = \frac{35.5 \text{ km}}{5 \text{ km per hour}} = 7.1 \text{ hours}
\][/tex]
So, it would take 7.1 hours for a man riding a bicycle at 5 km per hour to travel from Akosua’s village to Quamu.
