If a child ran into the road 65 to 70 feet ahead of you vehicle what is the highest speed from which you could stop could stop with good brakes?

You could stop at 20 miles per hour without hitting him.

---------------------

Assuming The Highway Code formula for stopping distances:

stopping_distance = thinking distance + stopping time

= speed + speed²/20 ft (where speed is in mph)

→ 65 = speed + speed²/20

→ speed² + 20speed + 1300 = 0

→ speed = -10 + 10√14 mph ≈ 27.4 mph

(The negative square root can be ignored as it gives a negative speed which is nonsense for this problem.)

However, this assumes that you observe, think and can start braking within 15/22 (≈ 0.68) seconds of the child running into the road (1ft for every 1 mph of speed), and your braking matches the Highway Code assumptions for good tyres, brakes and dry road conditions.