Question

Use the table below, which shows the speed of a train over a 3-hour period. The time count does not start from when the train began moving.

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

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

• A. 25%
• B. 100%
• C. 75%
• D. 125%

Hint:

Percentage increase always uses the starting value (speed at time 0) as the base, not the ending value.

Answer 1

The Correct Option is C

Step 1: Read off the starting and ending speeds.
From the table, at time 0 minutes the train's speed is 40 km/hour, and at time 180 minutes (the end of the 3-hour period) the speed is 70 km/hour.

Step 2: Apply the percentage increase formula.
Percentage increase is always calculated on the starting (original) value:
\[ \%\ \text{increase} = \frac{\text{final} - \text{initial}}{\text{initial}} \times 100 \]

Step 3: Substitute the values.
\[ \%\ \text{increase} = \frac{70-40}{40}\times 100 = \frac{30}{40}\times 100 = 75\% \]

Step 4: Rule out the other options.
Option 25% and option 100% do not match the calculation above. Option 125% would come from wrongly dividing 30 by 24 or a similar slip, not from the actual initial value of 40. Only 75% is correct.

Step 5: Final Answer.
The train's speed increased by 75% over the 3-hour period. \[ \boxed{75\%} \]