Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.
Solving realworld problems often requires a blend of logic and mathematical prowess. In this scenario, we delve into Ankita's journey home, exploring how she navigates the distance using a combination of rickshaw and bus. Let's unravel the mystery of Ankita's travel time and determine the speeds of the rickshaw and the bus.
Understanding the Given Scenario
Ankita's travel involves a 14 km distance, which she covers using both a rickshaw and a bus. The intriguing part is that the time taken varies based on the distance covered by each mode of transportation. When Ankita travels 2 km by rickshaw and the rest by bus, it takes her precisely half an hour. Conversely, if she opts for a 4 km rickshaw ride, the remaining distance by bus extends her journey by 9 minutes.
Setting Up Equations
To solve this puzzle, let's denote the speed of the rickshaw as $R$ and the speed of the bus as $B$. The equations based on the given conditions can be expressed as follows:
 $R2 +B12 =30$ (for the first scenario)
 $R4 +B10 =39$ (for the second scenario)
Solving the Equations
Now, let's apply our mathematical acumen to solve these equations systematically. By following a stepbystep process, we unveil the speeds of the rickshaw and the bus, providing a clear solution to Ankita's travel mystery.
Interpreting the Results
Upon solving the equations, we discover the speeds of the rickshaw and the bus. These numerical values hold significance, indicating how Ankita's travel time is influenced by the different modes of transport. Understanding these speeds is crucial in grasping the dynamics of her journey.
Realworld Implications
The ability to solve such mathematical problems transcends theoretical knowledge. Ankita's scenario mirrors everyday situations where a mix of transportation modes is involved. Mathematical skills, as demonstrated here, are essential in optimizing travel time and making informed decisions.
Importance of Rickshaw and Bus Speeds
Ankita's travel time is directly impacted by the speeds of the rickshaw and the bus. We delve into the broader implications of these speeds, shedding light on their significance not only for Ankita's journey but also in a general transportation context.
Utilizing the Information
The speeds we uncover are not just numbers; they hold practical utility. Understanding the rickshaw and bus speeds allows us to make informed decisions regarding travel routes, potentially saving time and enhancing overall efficiency.
Practical Implications
Beyond Ankita's specific scenario, the ability to solve problems involving multiple variables is a valuable skill. This scenario serves as a practical example of how mathematical thinking can be applied to realworld situations, emphasizing the importance of cultivating such problemsolving skills.
Let the speed of the rickshaw be x km/min and the speed of the bus be y km/min.
Since time = distance/speed,
2x+12y=30;
4x+10y=39.
Substituting 1x as u and 1y as v, we get (Where x≠0,y≠0)
2u+12v=30…(1)
4u+10v=39…(2)
Multiplying equation (1) by 2, we get 4u+24v=60…(3)
Subtracting equation (2) from equation (3), we get 14v = 21 ⇒v=32
Putting v=32 in equation (1), we get,
2u+12×32=30⇒2u=30−18
⇒u=122=6.
Therefore, x=16 km/min and y=23 km/min.
To get the speed in km/hr, we multiply each speed with 60, since 1 hr = 60 min.
Therefore,
x=16×60=10 km/hr
y=23×60=40 km/hr
Conclusion
In conclusion, Ankita's journey becomes a canvas for mathematical exploration. By deciphering the speeds of the rickshaw and the bus, we unravel the intricacies of her travel time. This exercise underscores the practical applications of mathematical thinking in everyday scenarios, encouraging us to approach problems with a systematic mindset.
FAQs

Q: How does Ankita's choice of transportation impact her travel time?
 A: Ankita's travel time is directly influenced by the speeds of the rickshaw and the bus, making her choice of transportation crucial.

Q: Are the obtained speeds applicable only to Ankita's scenario?
 A: While the speeds are specific to Ankita's situation, the problemsolving approach can be applied to similar scenarios.

Q: Can solving such mathematical problems have broader implications?
 A: Absolutely. Mathematical problemsolving skills are invaluable in various realworld situations beyond Ankita's journey.

Q: How can the information about rickshaw and bus speeds be practically utilized?
 A: Knowing these speeds can help in optimizing travel routes, potentially saving time and improving overall efficiency.

Q: What's the significance of understanding the broader applications of the solution?
 A: It highlights the versatility of mathematical thinking and encourages individuals to apply problemsolving skills in diverse contexts.