Math Problem Statement

A train crosses a 90 m long platform in 10 soc. If the length of the train is 60m thon find the spood of tho train?

Solution

To find the speed of the train, we first need to determine the total distance it covers when crossing the platform.

Step-by-step process:

  1. Length of the platform: 90 meters
  2. Length of the train: 60 meters
  3. Total distance covered by the train: When the train completely crosses the platform, it travels a distance equal to the length of the train plus the length of the platform. Total distance=60meters (train length)+90meters (platform length)=150meters\text{Total distance} = 60 \, \text{meters (train length)} + 90 \, \text{meters (platform length)} = 150 \, \text{meters}
  4. Time taken to cross the platform: 10 seconds
  5. Speed of the train: Speed is calculated using the formula: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}} Substituting the values: Speed=150meters10seconds=15m/s\text{Speed} = \frac{150 \, \text{meters}}{10 \, \text{seconds}} = 15 \, \text{m/s}

Thus, the speed of the train is 15 m/s.

Conversion to km/h:

If you want to convert this to kilometers per hour (km/h): Speed in km/h=15m/s×185=54km/h\text{Speed in km/h} = 15 \, \text{m/s} \times \frac{18}{5} = 54 \, \text{km/h}

The speed of the train is 54 km/h.


Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions for you to explore:

  1. How would the speed change if the length of the train was different?
  2. What would happen to the speed if the train crossed the platform in less time?
  3. How can you convert speed from km/h to m/s?
  4. How do you find the time if you know the speed and distance?
  5. What would be the speed if the platform length doubled?

Tip: Always make sure to include both the train and platform lengths when calculating total distance in such problems.

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Math Problem Analysis

Mathematical Concepts

Speed, Distance, and Time
Unit Conversion (m/s to km/h)

Formulas

Speed = Distance / Time
Speed in km/h = Speed in m/s × 18/5

Theorems

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Suitable Grade Level

Grades 6-8