Analyzing Train Data to Find Maximum Travel Time

To find out which train will take the maximum time to reach its destination, we need to use the information provided in the table, specifically the distance and speed for each train. The relationship between time, distance, and speed is given by the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

We need to calculate the time taken for each train mentioned in the options and then compare these times to find the maximum. The table provides the necessary data:

Calculating Travel Time for Each Train Option

Let's calculate the time taken for each train listed in the options:

• Train 1001: Distance = 1200 km, Speed = 130 km/h \[ \text{Time}_{1001} = \frac{1200 \text{ km}}{130 \text{ km/h}} = \frac{120}{13} \text{ hours} \approx 9.23 \text{ hours} \]
• Train 1003: Distance = 1280 km, Speed = 155 km/h \[ \text{Time}_{1003} = \frac{1280 \text{ km}}{155 \text{ km/h}} = \frac{256}{31} \text{ hours} \approx 8.26 \text{ hours} \]
• Train 1004: Distance = 1250 km, Speed = 130 km/h \[ \text{Time}_{1004} = \frac{1250 \text{ km}}{130 \text{ km/h}} = \frac{125}{13} \text{ hours} \approx 9.62 \text{ hours} \]
• Train 1005: Distance = 1180 km, Speed = 125 km/h \[ \text{Time}_{1005} = \frac{1180 \text{ km}}{125 \text{ km/h}} = \frac{236}{25} \text{ hours} = 9.44 \text{ hours} \]

Comparing the Calculated Times

Now, let's compare the approximate travel times for each train:

• Train 1001: $\approx 9.23$ hours
• Train 1003: $\approx 8.26$ hours
• Train 1004: $\approx 9.62$ hours
• Train 1005: $= 9.44$ hours

Comparing these values (9.23, 8.26, 9.62, 9.44), we can see that the maximum time is approximately 9.62 hours, which corresponds to Train 1004.

Therefore, Train 1004 will take the maximum time to reach its destination among the given options.

Revision Table: Train Time Calculation Summary

Additional Information: Understanding Time, Distance, and Speed

The relationship between time, distance, and speed is a fundamental concept in physics and everyday travel. It is often represented by the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

This formula can be rearranged to find any of the three variables if the other two are known:

• To find Distance: $\text{Distance} = \text{Speed} \times \text{Time}$
• To find Time: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
• To find Speed: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

It is crucial that the units are consistent when performing calculations. For example, if distance is in kilometers (km) and time is in hours (h), then speed must be in kilometers per hour (km/h). If speed were given in meters per second (m/s), you would need to convert units before calculating. In this question, the units (km and km/h) are consistent, making the direct application of the formula straightforward.