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: Note what "2 and a half hours" means in minutes.
Half an hour is 30 minutes, so $2\frac{1}{2}$ hours is $2\times 60+30=150$ minutes.

Step 2: Locate 150 minutes on the time axis of the table.
Scanning the top row of the table (0, 30, 45, 60, 90, 120, 150, 180), the value 150 appears directly as one of the given time marks.

Step 3: Read the matching speed.
Directly below 150 minutes in the speed row, the table shows 65 km/hour.

Step 4: Sanity check with the rate of change.
From $t=120$ (speed 60) to $t=150$ (30 minutes later), the speed should rise by $30\times\frac{1}{6}=5$ km/hour, taking it from 60 to 65 km/hour. This matches the table exactly, confirming the reading is correct.

Step 5: Final Answer.
The other three options (50, 55, 60 km/hour) belong to earlier time marks (60, 90, and 120 minutes respectively), not to 150 minutes, so they are incorrect.
\[ \boxed{65 \text{ km/h}} \]