Adam walks $$ 1,25 \mathrm{~km} $$ in 25 minutes and Sean 1,44 km in 30 minutes. Who walks faster? A bus departs from Bloemfontein to Durban and travels at an average speed of $$ 94 \mathrm{~km} / \mathrm{h} $$. The distance between the 2 cities is 116 km . How long will the trip take? A car departs at $$ 07: 00 $$ and travels at an average speed of $$ 115 \mathrm{~km} / \mathrm{h} $$. What time will it arrive at its destination which is $$ 632,5 \mathrm{~km} $$ away?

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UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### Part 1: Comparing Adam and Sean's Speeds

1. **Calculate Adam's speed:**
   - Distance = $$ 1.25 $$ km
   - Time = $$ 25 $$ minutes = $$ \frac{25}{60} $$ hours
   - Speed $$ v_A = \frac{\text{Distance}}{\text{Time}} = \frac{1.25}{\frac{25}{60}} $$

2. **Calculate Sean's speed:**
   - Distance = $$ 1.44 $$ km
   - Time = $$ 30 $$ minutes = $$ \frac{30}{60} $$ hours
   - Speed $$ v_S = \frac{\text{Distance}}{\text{Time}} = \frac{1.44}{\frac{30}{60}} $$

### Part 2: Calculate the Trip Time for the Bus

1. **Bus speed and distance:**
   - Speed = $$ 94 $$ km/h
   - Distance = $$ 116 $$ km
   - Time $$ t_B = \frac{\text{Distance}}{\text{Speed}} = \frac{116}{94} $$

### Part 3: Calculate Arrival Time for the Car

1. **Car speed and distance:**
   - Speed = $$ 115 $$ km/h
   - Distance = $$ 632.5 $$ km
   - Time $$ t_C = \frac{\text{Distance}}{\text{Speed}} = \frac{632.5}{115} $$

2. **Departure time:**
   - Departure at $$ 07:00 $$
   - Convert travel time to hours and minutes to find the arrival time.

Now, let's perform the calculations for each part.

### Calculations

1. **Adam's speed:**
   $$
   v_A = \frac{1.25}{\frac{25}{60}} = \frac{1.25 \times 60}{25} = 3 \text{ km/h}
   $$

2. **Sean's speed:**
   $$
   v_S = \frac{1.44}{\frac{30}{60}} = \frac{1.44 \times 60}{30} = 2.88 \text{ km/h}
   $$

3. **Bus trip time:**
   $$
   t_B = \frac{116}{94} \text{ hours}
   $$

4. **Car trip time:**
   $$
   t_C = \frac{632.5}{115} \text{ hours}
   $$

Now, I will calculate the exact values for $$ t_B $$ and $$ t_C $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{116}{94}$$
- step1: Reduce the fraction:
  $$\frac{58}{47}$$
Calculate or simplify the expression $$ 632.5/115 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{632.5}{115}$$
- step1: Convert the expressions:
  $$\frac{\frac{1265}{2}}{115}$$
- step2: Multiply by the reciprocal:
  $$\frac{1265}{2}\times \frac{1}{115}$$
- step3: Reduce the numbers:
  $$\frac{11}{2}\times 1$$
- step4: Multiply:
  $$\frac{11}{2}$$
### Results of the Calculations

1. **Adam's Speed:**
   - $$ v_A = 3 $$ km/h

2. **Sean's Speed:**
   - $$ v_S = 2.88 $$ km/h

**Conclusion for Part 1:**
- Adam walks faster than Sean since $$ 3 $$ km/h > $$ 2.88 $$ km/h.

---

3. **Bus Trip Time:**
   - $$ t_B \approx 1.234 $$ hours, which is approximately $$ 1 $$ hour and $$ 14 $$ minutes.

4. **Car Trip Time:**
   - $$ t_C = 5.5 $$ hours, which is $$ 5 $$ hours and $$ 30 $$ minutes.

### Arrival Time for the Car

- **Departure Time:** $$ 07:00 $$
- **Travel Time:** $$ 5 $$ hours and $$ 30 $$ minutes

To find the arrival time, we add $$ 5 $$ hours and $$ 30 $$ minutes to $$ 07:00 $$:

- $$ 07:00 + 5 \text{ hours} = 12:00 $$
- $$ 12:00 + 30 \text{ minutes} = 12:30 $$

### Final Summary

1. **Who walks faster?**
   - Adam walks faster at $$ 3 $$ km/h compared to Sean's $$ 2.88 $$ km/h.

2. **Bus trip duration:**
   - Approximately $$ 1 $$ hour and $$ 14 $$ minutes.

3. **Car arrival time:**
   - The car will arrive at $$ 12:30 $$.
Adam walks faster at 3 km/h. The bus trip takes about 1 hour and 14 minutes. The car will arrive at 12:30.

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