Understanding the Problem: Calculating Time from Distance and Speed

The question asks us to find the time Radha takes to cover a specific distance while running at a given speed. We are given the distance in meters and the speed in kilometers per hour. To solve this, we need to use the relationship between distance, speed, and time, and ensure all units are consistent.

Given Information:

• Distance (D) = 1950 meters (m)
• Speed (S) = 26 kilometers per hour (km/h)

We need to find the time (T) in minutes.

Unit Conversion for Consistency

The distance is in meters and the speed is in kilometers per hour. To use the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \), the units must be consistent. We can convert the speed from km/h to meters per minute (m/min) since the desired time unit is minutes and distance is in meters.

• 1 kilometer (km) = 1000 meters (m)
• 1 hour (h) = 60 minutes (min)

Let's convert the speed:

\( \text{Speed in m/min} = 26 \, \frac{\text{km}}{\text{h}} \)

\( \text{Speed in m/min} = 26 \times \frac{1000 \, \text{m}}{60 \, \text{min}} \)

\( \text{Speed in m/min} = \frac{26 \times 1000}{60} \, \frac{\text{m}}{\text{min}} \)

\( \text{Speed in m/min} = \frac{26000}{60} \, \frac{\text{m}}{\text{min}} \)

Cancel out a zero from the numerator and denominator:

\( \text{Speed in m/min} = \frac{2600}{6} \, \frac{\text{m}}{\text{min}} \)

Divide both by 2:

\( \text{Speed in m/min} = \frac{1300}{3} \, \frac{\text{m}}{\text{min}} \)

Now, the distance is in meters (1950 m) and the speed is in meters per minute (\( \frac{1300}{3} \) m/min). We can calculate the time in minutes.

Applying the Distance, Speed, Time Formula

The formula relating distance, speed, and time is:

\( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)

Substitute the values:

\( \text{Time} = \frac{1950 \, \text{m}}{\frac{1300}{3} \, \text{m/min}} \)

To divide by a fraction, multiply by its reciprocal:

\( \text{Time} = 1950 \times \frac{3}{1300} \, \text{min} \)

Simplify the expression:

\( \text{Time} = \frac{1950 \times 3}{1300} \, \text{min} \)

Cancel out a zero from 1950 and 1300:

\( \text{Time} = \frac{195 \times 3}{130} \, \text{min} \)

Notice that 195 and 130 are both divisible by 5:

• \(195 \div 5 = 39\)
• \(130 \div 5 = 26\)

\( \text{Time} = \frac{39 \times 3}{26} \, \text{min} \)

Notice that 39 and 26 are both divisible by 13:

• \(39 \div 13 = 3\)
• \(26 \div 13 = 2\)

\( \text{Time} = \frac{3 \times 3}{2} \, \text{min} \)

\( \text{Time} = \frac{9}{2} \, \text{min} \)

Convert the improper fraction to a mixed number:

\( \frac{9}{2} = 4 \frac{1}{2} \)

So, the time taken is \( 4 \frac{1}{2} \) minutes.

Conclusion

Radha will take \( 4 \frac{1}{2} \) minutes to cover a distance of 1950 m running at a speed of 26 km/h.

Revision Table: Distance Speed Time Calculations

Additional Information: Unit Conversion Tips

Converting units accurately is crucial in distance, speed, and time problems. Here are some key conversions:

• 1 km = 1000 m
• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 hour = 3600 seconds (60 min \(\times\) 60 sec/min)

To convert speed from km/h to m/s, you can multiply by \( \frac{1000 \, \text{m}}{3600 \, \text{s}} \), which simplifies to multiplying by \( \frac{5}{18} \).

To convert speed from m/s to km/h, you can multiply by \( \frac{3600 \, \text{s}}{1000 \, \text{m}} \), which simplifies to multiplying by \( \frac{18}{5} \).

In this problem, converting km/h to m/min was direct: multiply by \( \frac{1000 \, \text{m}}{60 \, \text{min}} \).