Car travels 80km in 25mph. Cost is 5p a minute. Bus takes a 5 min stop and arrives at same time as car. Cost is 20% more expensice per minute than car. Train travels three times faster than car, is 3x more espesive. The  cylist trabels 1/5 as fast as train. Cost is 5% of the cost of running a train. 1 mile is 1.6 km. Speed is distnace divided by time. How much more cost the train than cyclsit

To calculate how much more the train costs compared to the cyclist, we need to follow a step-by-step approach by analyzing the given data and applying the necessary formulas.

### 1. Convert Car's Speed from mph to km/h:
The car's speed is given as 25 mph. To convert to km/h:

\[
1 \text{ mile} = 1.6 \text{ km}
\]
\[
25 \text{ mph} = 25 \times 1.6 = 40 \text{ km/h}
\]

So, the car travels at 40 km/h.

### 2. Find the Time for Car to Travel 80 km:
Using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
For the car:
\[
\text{Time for car} = \frac{80 \text{ km}}{40 \text{ km/h}} = 2 \text{ hours}
\]

### 3. Calculate Cost of Car Travel:
The cost of the car travel is 5p per minute, so we need to convert the car's time of travel into minutes. 

\[
2 \text{ hours} = 2 \times 60 = 120 \text{ minutes}
\]

Thus, the cost of the car's travel is:
\[
\text{Cost of car travel} = 120 \times 5 \text{p} = 600 \text{p} = £6
\]

### 4. Bus's Travel Time and Cost:
The bus arrives at the same time as the car but takes a 5-minute stop. Therefore, the actual time the bus travels is:
\[
\text{Time for bus travel} = 120 - 5 = 115 \text{ minutes}
\]

The bus is 20% more expensive per minute than the car, so the cost per minute for the bus is:
\[
\text{Bus cost per minute} = 5 \text{p} + 20\% \times 5 \text{p} = 5 \text{p} + 1 \text{p} = 6 \text{p}
\]

Thus, the total cost of the bus is:
\[
\text{Cost of bus travel} = 115 \times 6 \text{p} = 690 \text{p} = £6.90
\]

### 5. Train's Travel Time and Cost:
The train travels **three times faster** than the car. Therefore, the speed of the train is:
\[
\text{Train speed} = 3 \times 40 \text{ km/h} = 120 \text{ km/h}
\]

The time taken by the train to travel 80 km is:
\[
\text{Time for train travel} = \frac{80}{120} = \frac{2}{3} \text{ hours} = 40 \text{ minutes}
\]

The cost of running the train is three times more expensive than the car, so the cost per minute for the train is:
\[
\text{Train cost per minute} = 3 \times 5 \text{p} = 15 \text{p}
\]

Thus, the total cost of the train travel is:
\[
\text{Cost of train travel} = 40 \times 15 \text{p} = 600 \text{p} = £6
\]

### 6. Cyclist's Travel Time and Cost:
The cyclist travels **1/5** as fast as the train, so the speed of the cyclist is:
\[
\text{Cyclist speed} = \frac{1}{5} \times 120 \text{ km/h} = 24 \text{ km/h}
\]

The time taken by the cyclist to travel 80 km is:
\[
\text{Time for cyclist travel} = \frac{80}{24} \approx 3.33 \text{ hours} = 3.33 \times 60 \approx 200 \text{ minutes}
\]

The cost of running the cyclist is 5% of the cost of running the train. Since the train costs 15p per minute:
\[
\text{Cyclist cost per minute} = 0.05 \times 15 \text{p} = 0.75 \text{p}
\]

Thus, the total cost of the cyclist travel is:
\[
\text{Cost of cyclist travel} = 200 \times 0.75 \text{p} = 150 \text{p} = £1.50
\]

### 7. Final Comparison: How Much More the Train Costs than the Cyclist
\[
\text{Difference in cost} = £6 - £1.50 = £4.50
\]

### Conclusion:
The train costs £4.50 more than the cyclist.

---

Would you like further details or have any questions?

Here are 5 related questions:
1. How much time does each vehicle take to complete the journey?
2. How would the costs change if the train were only twice as fast?
3. What is the total cost of travel for all four modes of transport?
4. If the cyclist's cost per minute increased by 10%, how much would it cost to travel the same distance?
5. How does the speed of the car compare with the cyclist’s speed in terms of a ratio?

**Tip**: Always break down word problems into smaller, manageable steps to ensure you account for all the details.

Car travels 80km in 25mph. Cost is 5p a minute. Bus takes a 5 min stop and arrives at same time as car. Cost is 20% more expensive per minute than car. Train travels three times faster than car, is 3x more expensive. The cyclist travels 1/5 as fast as train. Cost is 5% of the cost of running a train. 1 mile is 1.6 km. Speed is distance divided by time. How much more does the train cost than cyclist?

Analyze the cost difference between a train and a cyclist traveling 80 km. This detailed solution involves unit conversions, speed, time, and cost calculations. Explore how the train is faster and more expensive than the cyclist, using percentages and real-world cost factors. Ideal for Grades 9-12 students.

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