Calculating Ram's Speed from Distance and Time

This problem requires us to calculate Ram's speed given the distance he traveled and the time taken. The distance is given in meters and the time in minutes and seconds, but the desired speed unit is kilometers per hour (km/h). Therefore, the first step is to convert the given units to kilometers and hours before calculating the speed.

Converting Units for Speed Calculation

Converting Distance to Kilometers

The distance Ram traveled is 900 meters. To convert meters to kilometers, we use the conversion factor:

1 kilometer (km) = 1000 meters (m)

So, to convert 900 meters to kilometers, we divide by 1000:

$$ \text{Distance} = 900 \text{ m} \times \left( \frac{1 \text{ km}}{1000 \text{ m}} \right) = \frac{900}{1000} \text{ km} = 0.9 \text{ km} $$

The distance is 0.9 km.

Converting Time to Hours

The time taken is 15 minutes and 30 seconds. To convert this time into hours, we first convert everything into seconds and then convert seconds into hours.

First, convert minutes to seconds:

1 minute = 60 seconds

$$ 15 \text{ minutes} = 15 \times 60 \text{ seconds} = 900 \text{ seconds} $$

Now, add the extra 30 seconds:

$$ \text{Total time in seconds} = 900 \text{ seconds} + 30 \text{ seconds} = 930 \text{ seconds} $$

Next, convert total seconds to hours. We know that:

1 hour = 60 minutes = 60 × 60 seconds = 3600 seconds

To convert 930 seconds to hours, we divide by 3600:

$$ \text{Time} = 930 \text{ seconds} \times \left( \frac{1 \text{ hour}}{3600 \text{ seconds}} \right) = \frac{930}{3600} \text{ hours} $$

The time taken is $\frac{930}{3600}$ hours.

Calculating Ram's Speed

Applying the Speed Formula

The formula for speed is:

$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$

We have the distance in km (0.9 km) and the time in hours ($\frac{930}{3600}$ hours). Now, we can calculate the speed in km/h:

$$ \text{Speed} = \frac{0.9 \text{ km}}{\frac{930}{3600} \text{ hours}} $$

To simplify the expression, we can multiply by the reciprocal of the denominator:

$$ \text{Speed} = 0.9 \times \frac{3600}{930} \text{ km/h} $$

$$ \text{Speed} = \frac{0.9 \times 3600}{930} \text{ km/h} $$

$$ \text{Speed} = \frac{3240}{930} \text{ km/h} $$

Now, we perform the division:

$$ \text{Speed} \approx 3.48387... \text{ km/h} $$

Rounding to Two Decimal Places

The question asks for the speed correct to two decimal places. Looking at the third decimal place (which is 3), we round down.

$$ \text{Speed} \approx 3.48 \text{ km/h} $$

Ram's speed is approximately 3.48 km/h.

Ram's Speed Calculation Revision Table

Additional Speed Calculation Information

Understanding the relationship between speed, distance, and time is fundamental in physics and everyday calculations. The formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ can be rearranged to find distance ($\text{Distance} = \text{Speed} \times \text{Time}$) or time ($\text{Time} = \frac{\text{Distance}}{\text{Speed}}$) if the other two quantities are known.

It is crucial to use consistent units when performing calculations. For instance, if you use distance in kilometers, the time must be in hours to get the speed in km/h. If you use distance in meters and time in seconds, the speed will be in meters per second (m/s). You can then convert m/s to km/h using the conversion factor: $1 \text{ m/s} = 3.6 \text{ km/h}$ (since $1 \text{ m} = 1/1000 \text{ km}$ and $1 \text{ s} = 1/3600 \text{ hour}$, so $1 \text{ m/s} = \frac{1/1000 \text{ km}}{1/3600 \text{ hour}} = \frac{1}{1000} \times 3600 \text{ km/h} = \frac{3600}{1000} \text{ km/h} = 3.6 \text{ km/h}$).

In this problem, converting to km and hours first simplified the final calculation to directly yield the result in the desired unit.