Yug covers a certain distance with a speed of 56 km/h in \(\frac{3}{2}\) hours. If he wants to cover the same distance in 7 hours, what would be his speed (in km/h)?
12
Calculating Speed with Distance and Time
This problem involves the fundamental relationship between speed, distance, and time. The formula connecting these three quantities is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
From this formula, we can also derive expressions for speed and time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this question, Yug first covers a certain distance at a given speed and time. We need to calculate this distance first.
Step 1: Calculate the total distance covered
Yug's initial speed is given as 56 km/h, and the time taken is \(\frac{3}{2}\) hours.
Using the formula Distance = Speed \(\times\) Time:
\[ \text{Distance} = 56 \text{ km/h} \times \frac{3}{2} \text{ hours} \]
\[ \text{Distance} = 56 \times \frac{3}{2} \text{ km} \]
\[ \text{Distance} = \frac{56 \times 3}{2} \text{ km} \]
\[ \text{Distance} = 28 \times 3 \text{ km} \]
\[ \text{Distance} = 84 \text{ km} \]
So, the distance covered by Yug is 84 km.
Step 2: Calculate the new speed required
Now, Yug wants to cover the same distance (84 km) in a new time of 7 hours. We need to find the new speed required for this.
Using the formula Speed = \(\frac{\text{Distance}}{\text{Time}}\):
\[ \text{New Speed} = \frac{\text{Distance}}{\text{New Time}} \]
\[ \text{New Speed} = \frac{84 \text{ km}}{7 \text{ hours}} \]
\[ \text{New Speed} = \frac{84}{7} \text{ km/h} \]
\[ \text{New Speed} = 12 \text{ km/h} \]
Thus, Yug's new speed needs to be 12 km/h to cover the distance of 84 km in 7 hours.
Summary of Calculations
| Parameter | Initial Scenario | New Scenario |
|---|---|---|
| Speed | 56 km/h | ? km/h (To be calculated) |
| Time | \(\frac{3}{2}\) hours | 7 hours |
| Distance | Calculated as 84 km | Same distance (84 km) |
The required new speed is 12 km/h.
Revision Table: Speed, Distance, and Time Formulas
| Concept | Formula |
|---|---|
| Distance | Speed \(\times\) Time |
| Speed | \(\frac{\text{Distance}}{\text{Time}}\) |
| Time | \(\frac{\text{Distance}}{\text{Speed}}\) |
Additional Information: Inverse Relationship
For a fixed distance, speed and time are inversely proportional. This means if you want to cover the same distance in less time, you need to increase your speed. Conversely, if you take more time to cover the same distance, your speed must decrease.
In this problem, the time increases from \(\frac{3}{2}\) hours (1.5 hours) to 7 hours. Since the time increases, the speed must decrease. The initial speed was 56 km/h, and the new speed is 12 km/h, which is a decrease, confirming the inverse relationship principle.
Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
