A bike consumes 20 mL of petrol per kilometre, if it is driven at a speed in the range of 25 – 50 km/hour and consumes 40 mL of petrol per kilometre at any other speed. How much petrol is consumed by the bike in travelling a distance of 50 km, if the bike is driven at a speed of 40 km/hour for the first 10 km, at a speed of 60 km/hour for the next 30 km and at a speed of 30 km/hour for the last 10 km?
1.6 L
Calculating Bike Petrol Consumption Based on Speed
This problem asks us to calculate the total amount of petrol consumed by a bike travelling a total distance of 50 km. The key factor influencing petrol consumption is the bike's speed during different parts of the journey.
Understanding Petrol Consumption Rules
The problem provides specific rules for petrol consumption based on the bike's speed:
- If the speed is in the range of 25 km/hour to 50 km/hour (inclusive of 25 and 50), the consumption rate is 20 mL of petrol per kilometre (\(\text{mL/km}\)).
- If the speed is outside this range (either below 25 km/hour or above 50 km/hour), the consumption rate is higher, specifically 40 mL of petrol per kilometre (\(\text{mL/km}\)).
Analyzing the Journey Segments
The total distance of 50 km is covered in three distinct segments, each with a different speed:
- The first 10 km are covered at a speed of 40 km/hour.
- The next 30 km are covered at a speed of 60 km/hour.
- The last 10 km are covered at a speed of 30 km/hour.
We need to determine the petrol consumption rate for each segment based on the speed and then calculate the petrol consumed in each segment.
Calculating Consumption for Each Segment
Segment 1: First 10 km
- Distance: 10 km
- Speed: 40 km/hour
- Speed analysis: 40 km/hour is within the range of 25 – 50 km/hour.
- Consumption rate for this segment: 20 mL/km.
- Petrol consumed in Segment 1: \[ \text{Consumption}_1 = \text{Distance}_1 \times \text{Rate}_1 \] \[ \text{Consumption}_1 = 10 \text{ km} \times 20 \text{ mL/km} \] \[ \text{Consumption}_1 = 200 \text{ mL} \]
Segment 2: Next 30 km
- Distance: 30 km
- Speed: 60 km/hour
- Speed analysis: 60 km/hour is outside the range of 25 – 50 km/hour (it is greater than 50 km/hour).
- Consumption rate for this segment: 40 mL/km.
- Petrol consumed in Segment 2: \[ \text{Consumption}_2 = \text{Distance}_2 \times \text{Rate}_2 \] \[ \text{Consumption}_2 = 30 \text{ km} \times 40 \text{ mL/km} \] \[ \text{Consumption}_2 = 1200 \text{ mL} \]
Segment 3: Last 10 km
- Distance: 10 km
- Speed: 30 km/hour
- Speed analysis: 30 km/hour is within the range of 25 – 50 km/hour.
- Consumption rate for this segment: 20 mL/km.
- Petrol consumed in Segment 3: \[ \text{Consumption}_3 = \text{Distance}_3 \times \text{Rate}_3 \] \[ \text{Consumption}_3 = 10 \text{ km} \times 20 \text{ mL/km} \] \[ \text{Consumption}_3 = 200 \text{ mL} \]
Calculating Total Petrol Consumption
To find the total petrol consumed for the entire 50 km journey, we add the consumption from each segment:
\[ \text{Total Consumption} = \text{Consumption}_1 + \text{Consumption}_2 + \text{Consumption}_3 \] \[ \text{Total Consumption} = 200 \text{ mL} + 1200 \text{ mL} + 200 \text{ mL} \] \[ \text{Total Consumption} = 1600 \text{ mL} \]Converting Millilitres to Litres
The total consumption is 1600 mL. We are typically asked to give the answer in Litres. We know that 1 Litre (\(\text{L}\)) is equal to 1000 Millilitres (\(\text{mL}\)).
\[ 1 \text{ L} = 1000 \text{ mL} \]To convert 1600 mL to Litres, we divide by 1000:
\[ \text{Total Consumption (L)} = \frac{1600 \text{ mL}}{1000 \text{ mL/L}} \] \[ \text{Total Consumption (L)} = 1.6 \text{ L} \]So, the total petrol consumed by the bike in travelling the distance of 50 km is 1.6 Litres.
Summary of Petrol Consumption Calculation
| Segment | Distance (km) | Speed (km/hour) | Speed Range (25-50 km/h)? | Consumption Rate (mL/km) | Petrol Consumed (mL) |
|---|---|---|---|---|---|
| 1 | 10 | 40 | Yes | 20 | \(10 \times 20 = 200\) |
| 2 | 30 | 60 | No | 40 | \(30 \times 40 = 1200\) |
| 3 | 10 | 30 | Yes | 20 | \(10 \times 20 = 200\) |
Total Consumption = \(200 \text{ mL} + 1200 \text{ mL} + 200 \text{ mL} = 1600 \text{ mL} = 1.6 \text{ L}\).
Revision Table: Key Concepts
| Concept | Explanation | Application in Problem |
|---|---|---|
| Petrol Consumption Rate | Amount of fuel used per unit distance (e.g., mL/km). | Given as 20 mL/km or 40 mL/km depending on speed. |
| Speed Ranges & Consumption | Fuel efficiency changes with speed; different speed ranges have different consumption rates. | < 25 or > 50 km/h consumes more (40 mL/km); 25-50 km/h consumes less (20 mL/km). |
| Distance & Consumption | Total consumption = Distance \(\times\) Consumption Rate. | Calculated for each segment and summed up. |
| Unit Conversion (mL to L) | 1 Litre = 1000 Millilitres. | Used to convert the final answer from mL to L. |
Additional Information on Bike Fuel Efficiency
Bike petrol consumption is affected by many factors besides speed, such as:
- Riding Style: Aggressive acceleration and sudden braking increase fuel usage. Smooth riding is more efficient.
- Bike Maintenance: Proper tire pressure, clean air filter, well-tuned engine, and correct chain lubrication can significantly improve mileage.
- Road Conditions: Riding on rough roads or uphill requires more power, thus consuming more fuel.
- Load: Carrying heavier loads increases the effort required by the engine, leading to higher consumption.
- Traffic Conditions: Frequent stopping and starting in heavy traffic burns more fuel compared to steady riding.
- Engine Condition: An older or poorly maintained engine may be less fuel-efficient.
Understanding these factors can help riders optimize their fuel consumption and improve bike fuel efficiency in real-world conditions.
Similar Questions
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Important Questions from Relative Speed
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A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
Ram traveling at the speed of 3 km/h reaches 15 minutes late. Had he walked at 4 km/h, he would have reached 15 minutes earlier. How much distance does Ram have to cover?
