Sure, let's break down the problem step-by-step:
### (i) Calculating the Distance from Akosua's Village to Quamu
1. Walking Distance:
- Rate: [tex]\( 1 \frac{1}{2} \)[/tex] kilometers per hour (which is 1.5 kilometers per hour when converted to a decimal).
- Time: 3 hours.
- Distance = Rate × Time
[tex]\[
\text{Distance walked} = 1.5 \text{ km/hr} \times 3 \text{ hours} = 4.5 \text{ kilometers}
\][/tex]
2. Bus Distance:
- Rate: [tex]\( 15 \frac{1}{2} \)[/tex] kilometers per hour (which is 15.5 kilometers per hour when converted to a decimal).
- Time: 2 hours.
- Distance = Rate × Time
[tex]\[
\text{Distance by bus} = 15.5 \text{ km/hr} \times 2 \text{ hours} = 31.0 \text{ kilometers}
\][/tex]
3. Total Distance from Akosua's Village to Quamu:
- Total Distance = Walking Distance + Bus Distance
[tex]\[
\text{Total Distance} = 4.5 \text{ km} + 31.0 \text{ km} = 35.5 \text{ kilometers}
\][/tex]
### (ii) Calculating the Time Taken by Bicycle to Travel from Akosua's Village to Quamu
1. Total Distance:
- As calculated above, the total distance from Akosua's village to Quamu is 35.5 kilometers.
2. Bicycle Rate:
- Rate: 5 kilometers per hour.
3. Time = Distance / Rate
[tex]\[
\text{Time taken by bicycle} = \frac{35.5 \text{ kilometers}}{5 \text{ km/hr}} = 7.1 \text{ hours}
\][/tex]
### Summary of Solutions:
1. Distance from Akosua's village to Quamu:
[tex]\[
\text{Total Distance} = 35.5 \text{ kilometers}
\][/tex]
2. Time taken by a man riding a bicycle at 5 km/hr:
[tex]\[
\text{Time taken by bicycle} = 7.1 \text{ hours}
\][/tex]
So, Akosua’s village is 35.5 kilometers away from Quamu, and 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.
