Two cars travel the same distance starting at $10:00$ am and $11:00$ am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least $6$ hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

$20$

$25$

$30$

$10$

✅ Correct Option: 1

Two cars travel the same distance but start at different times:

First car: Starts at 10:00 am

Second car: Starts at 11:00 am (1 hour later)

Both reach the destination at the same time

Both travel the same distance

Let us define variables:

Let the first car travel for $t$ hours (where $t \geq 6$ )

Since the second car starts 1 hour later but they finish together, the second car travels for $(t-1)$ hours

Let $v_1$ = speed of first car, $v_2$ = speed of second car

Since both cars travel the same distance:

Distance = $v_1 \times t = v_2 \times (t-1)$

From this relationship:

$v_2 = v_1 \times \frac{t}{t-1}$

The percentage by which the second car's speed exceeds the first car's speed is:

Percentage increase = $\frac{v_2 - v_1}{v_1} \times 100\%$

Substituting our expression for $v_2$ :

$= \frac{v_1 \times \frac{t}{t-1} - v_1}{v_1} \times 100\%$

$= \left(\frac{t}{t-1} - 1\right) \times 100\%$

$= \frac{1}{t-1} \times 100\%$

To maximize this percentage, we need to minimize $(t-1)$ , which means minimizing $t$ .

Since the problem states the first car traveled for at least 6 hours, the minimum value of $t$ is 6.

When $t = 6$ :

Maximum percentage = $\frac{1}{6-1} \times 100\% = \frac{1}{5} \times 100\% = 20\%$

The longer the first car travels, the smaller the speed difference becomes. This makes intuitive sense: if both cars travel the same distance but the time difference between them stays constant (1 hour), the speed advantage of the second car becomes relatively smaller as the total travel time increases.

Therefore, the highest possible percentage by which the second car's speed could exceed the first car's speed is 20%.

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