Understanding the Problem: Calculating Distance from Speed and Time

The question asks us to find the distance Ramesh runs in metres, given his speed in kilometres per hour (kmph) and the time in minutes. To solve this, we need to ensure all units are consistent. The speed is given in km/h, and the time is in minutes, but we need the distance in metres. Therefore, we must convert the given speed and time into units that will result in distance in metres.

Given Information

• Ramesh's Speed = 234 kmph
• Time taken = 10 minutes

Unit Conversion Strategy

To find the distance in metres, it's easiest to convert the speed from kilometres per hour (km/h) to metres per second (m/s) and the time from minutes to seconds. Alternatively, we could convert speed to metres per minute, but m/s is a standard conversion.

Converting Speed from km/h to m/s

We know that:

• 1 kilometre (km) = 1000 metres (m)
• 1 hour (h) = 60 minutes = $60 \times 60$ seconds = 3600 seconds (s)

So, to convert speed from km/h to m/s, we can use the conversion factor:

$\text{Speed (m/s)} = \text{Speed (km/h)} \times \frac{1000 \, \text{m}}{3600 \, \text{s}}$

This simplifies to:

$\text{Speed (m/s)} = \text{Speed (km/h)} \times \frac{5}{18}$

Let's apply this to Ramesh's speed:

Speed = 234 km/h

Speed in m/s = $234 \times \frac{5}{18}$

We can simplify the calculation:

Speed in m/s = $\left(\frac{234}{18}\right) \times 5$

$234 \div 18 = 13$

Speed in m/s = $13 \times 5 = 65$ m/s

So, Ramesh runs at a speed of 65 metres per second.

Converting Time from Minutes to Seconds

We are given the time in minutes:

Time = 10 minutes

We know that:

• 1 minute = 60 seconds

So, to convert time from minutes to seconds:

Time in seconds = Time in minutes $\times$ 60

Time in seconds = $10 \times 60 = 600$ seconds

So, Ramesh runs for 600 seconds.

Calculating the Distance

The relationship between distance, speed, and time is given by the formula:

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

Now we have the speed in m/s and the time in seconds, which are consistent units:

• Speed = 65 m/s
• Time = 600 seconds

Let's calculate the distance:

Distance = $65 \, \text{m/s} \times 600 \, \text{s}$

Distance = $65 \times 600$ metres

Distance = $39000$ metres

Final Answer

Ramesh runs 39000 metres in ten minutes.

Revision Table: Speed, Distance, and Time Concepts

Additional Information: Understanding Unit Consistency

In physics and mathematics problems involving quantities like speed, distance, and time, it is crucial to ensure that the units are consistent before performing calculations. If speed is in kilometres per hour and time is in seconds, you cannot directly multiply them. You must convert one or both quantities so that their units align. For example, if you want the distance in metres, and speed is in m/s, your time must be in seconds. If speed is in km/h, and you want distance in km, your time must be in hours.

Common conversions:

• Length: 1 km = 1000 m
• Time: 1 minute = 60 seconds, 1 hour = 60 minutes = 3600 seconds
• Speed: Conversion between km/h and m/s is very common in problems. The factor $\frac{5}{18}$ comes directly from $\frac{1000 \text{ m}}{3600 \text{ s}}$.

Paying attention to units is a common source of errors in calculations, so always double-check your units before applying the formula.