Ralph and Steve took part in a cycling race. Both of them did not change their speed throughout the race. Ralph cycled at a speed of 20 km/h. When Steve covered half the distance, Ralph was 3.5 km in front of him. Ralph reached the finishing line at 10.45 a.m. What time did Steve reach the finishing line? Ans: ___

1. Determine the extra distance Ralph would travel in the time Steve takes to complete the race.

When Steve covers half the race distance, Ralph is $3.5\text{ km}$ ahead.
Since both cycle at constant speeds, in the time Steve takes to cover the full distance, Ralph would be $3.5 \times 2 = 7\text{ km}$ ahead of Steve.
This means in the time Steve takes to finish the race ($t_S$), Ralph would have travelled the full race distance plus an extra $7\text{ km}$.

2. Calculate the time difference between Steve and Ralph finishing the race.

Let the race distance be $D$.
Distance Ralph travels in Steve's total time $t_S$ is $D + 7$.
Distance Ralph travels in his own total time $t_R$ is $D$.
The difference in distance is $7\text{ km}$, which Ralph covers at his speed of $20\text{ km/h}$.
Time difference $= t_S - t_R = \frac{7}{20}\text{ hours}$.
$\frac{7}{20} \times 60 = 21\text{ minutes}$.
So, Steve takes $21\text{ minutes}$ longer than Ralph to finish the race.

3. Find the time Steve reached the finishing line.

Ralph finished at $10.45\text{ a.m.}$
Steve finished $21\text{ minutes}$ later.
$10.45\text{ a.m.} + 21\text{ minutes} = 11.06\text{ a.m.}$