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 journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
