Question

During the three-hour period shown in the table, the speed of the train increased by

• A. 25%
• B. 100%
• C. 75%
• D. 125%
• A. \(\frac{t}{6}\)
• B. 6t
• C. 40 + t
• D. 40+\(\frac{t}{6}\)
• A. 50 km/hr
• B. 55 km/hr
• C. 60 km/hr
• D. 65 km/hr

Answer 1

The Correct Option is C

Step 1: Understand the problem
We need to calculate the percentage increase in the train’s speed during the 3-hour period. The table gives the speed at the beginning (time 0) and at the end (time 180 minutes).

Step 2: Identify initial and final speeds
- Initial speed at 0 minutes = 40 km/hr
- Final speed at 180 minutes = 70 km/hr

Step 3: Calculate the increase in speed
Increase in speed = Final speed – Initial speed
= 70 – 40
= 30 km/hr

Step 4: Calculate percentage increase
Percentage increase = (Increase ÷ Initial speed) × 100
= (30 ÷ 40) × 100
= 0.75 × 100
= 75%

Step 5: Conclusion
Therefore, over the given 3-hour period, the train’s speed increased by 75%.

Final Answer: The correct option is (C): 75%

Answer 2

Step 1: Understand the problem
We are asked to find a formula that represents the speed of the train (in km/hr) at time t minutes after the beginning of the observation period. The table shows a steady increase in speed, so we are looking for a linear relationship between speed and time.

Step 2: Identify starting point
At t = 0 minutes, speed = 40 km/hr.
So the formula must give 40 when t = 0.

Step 3: Identify the rate of increase
At t = 180 minutes, speed = 70 km/hr.
Thus, total increase = 70 – 40 = 30 km/hr.
Time taken for this increase = 180 minutes.
Rate of increase = 30 ÷ 180 = 1/6 km/hr per minute.

Step 4: Formulate the equation
Speed at time t = Initial speed + (Increase per minute × t)
= 40 + (t ÷ 6).

Step 5: Verification
- At t = 0 → Speed = 40 + 0 = 40 (matches table).
- At t = 180 → Speed = 40 + (180 ÷ 6) = 40 + 30 = 70 (matches table).
- At t = 90 → Speed = 40 + (90 ÷ 6) = 40 + 15 = 55 (matches table).

Step 6: Conclusion
This confirms that the linear formula correctly represents the speed values in the table.

Final Answer: The correct option is (D): 40 + \(\frac{t}{6}\)

Answer 3

Step 1: Understand the problem
We need to calculate the speed of the train at 2½ hours (that is 2 hours and 30 minutes) after the beginning of the observation period. Using the formula derived earlier, speed at time t (in minutes) is: Speed = 40 + (t ÷ 6).

Step 2: Convert hours to minutes
2½ hours = 2 × 60 + 30 = 150 minutes.

Step 3: Apply the formula
Speed = 40 + (t ÷ 6)
= 40 + (150 ÷ 6)
= 40 + 25
= 65 km/hr.

Step 4: Verification with table
At 150 minutes, the table already gives the speed as 65 km/hr. This matches perfectly with our calculation.

Step 5: Conclusion
Therefore, the train was travelling at 65 km/hr after 2½ hours (150 minutes).

Final Answer: The correct option is (D): 65 km/hr