Question

Use the same train-speed table as above.

Time (minutes)	0	30	45	60	90	120	150	180
Speed (km/hour)	40	45	47.5	50	55	60	65	70

How fast was the train travelling \(2\frac{1}{2}\) hours after the beginning of the time period?

• A. 50 km/h
• B. 55 km/h
• C. 60 km/h
• D. 65 km/h

Hint:

Convert \(2\frac{1}{2}\) hours to 150 minutes and read that column straight off the table.

Answer 1

The Correct Option is D

Step 1: Convert the time to minutes.
\(2\frac{1}{2}\) hours equals \(2.5\times 60=150\) minutes.

Step 2: Read the table directly.
The table has a column for \(t=150\) minutes, and the speed listed there is 65 km/hour. Since this value is given directly in the table, we do not even need a formula to answer this question.

Step 3: Cross-check using the linear formula from the previous question.
Using \(v(t)=40+\frac{t}{6}\):
\[ v(150) = 40+\frac{150}{6} = 40+25 = 65 \text{ km/hour} \]
Both methods agree.

Step 4: Rule out the other options.
50 km/hour is the speed at \(t=60\) minutes (1 hour), 55 km/hour is the speed at \(t=90\) minutes (1.5 hours), and 60 km/hour is the speed at \(t=120\) minutes (2 hours). None of these correspond to \(t=150\) minutes.

Step 5: Final Answer.
At \(2\frac{1}{2}\) hours (150 minutes), the train was travelling at 65 km/hour. \[ \boxed{65 \text{ km/h}} \]