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: Compare the two speeds as a ratio.
Instead of computing the increase directly, look at how many times bigger the final speed is compared to the starting speed. Initial speed = 40 km/hour, final speed (at 180 minutes) = 70 km/hour.
\[ \frac{\text{final}}{\text{initial}} = \frac{70}{40} = 1.75 \]

Step 2: Convert the ratio to a percentage increase.
A ratio of 1.75 means the final speed is 175% of the initial speed. The increase over the original 100% is therefore $175\%-100\%=75\%$.

Step 3: Cross-check with the raw numbers.
The actual rise in speed is $70-40=30$ km/hour. As a fraction of the original 40 km/hour, that is $30/40=0.75$, which is again 75%. Both routes agree.

Step 4: Match to the options.
None of 25%, 100% or 125% equal 75%, so those are eliminated.
\[ \boxed{75\%} \]