This question seems so simple yet I'm having trouble understanding how to get the answers

Question

Sergio runs a 100-meter race. 7 seconds after the race started Sergio is 35 meters from the starting line and reaches his max speed; he runs at this max speed for the rest of the race. Sergio notices that he is 70 meters from the starting line 12 seconds after the race started.

What is Sergio's max speed?

Suppose Sergio runs for an additional  seconds after reaching his max speed...

How far will Sergio travel during those additional  seconds?

What is Sergio's distance from the starting line  seconds after the race started?

What is Sergio's distance from the starting line 

 seconds after the race started (provided 

)?

Answer 1

Let d(x) denote Sergio's distance (in meters) from the starting line x seconds after the race started. If v is his max speed, then Sergio's displacement after 7 seconds is v(x - 7). Thus, d(x) - 35 = v(x - 7) for x >= 7. Since d = 70 when t = 12, we find 70 - 35 = v(12 - 7), or 35 = 5v. Therefore, v = 7 meters per second and

d(x) = 35 + 7(x - 7), x >= 7

During the additional z seconds, Sergio will travel 7z meters. His distance from the starting line 7 + z seconds after the race has started is 35 + 7z.

Answer 2

We can see that after reaching max speed, Sergio travels 35 additional meters (70m - 35m) in 5 seconds (12s- 7s). That means his max speed is 35/5 = 7 m/s.

If he runs an additional z seconds at max speed of 7m/s, then he will cover 7 * Z additional meters.

I think with those answers, the rest of the problem is very easily worked.