We are given three pieces of information. The hare's speed, the tortoise's speed, and the head start that the tortoise has. The units are feet/second for speed and feet for distance. Time will then be in seconds.
The principle is DISTANCE = RATE • TIME, or D = R • T
The rate is the same as the speed.
For the hare, DHare = 50 • T
That is the distance (feet) the hare travels in t seconds.
For the tortoise, DTortoise = .25 • T + 1000
The tortoise gets 1000 added to the distance equation because of the 1000 foot head start.
They well be at the same distance from the starting line when those equations are equal to each other.
50 • T = .25 • T + 1000
Subtract .25 • T from each side:
50 • T - .25 • T = .25 • T + 1000 - .25 • T
49.75 • T = 1000
Divide both sides by 49.75:
T = 1000 / 49.75
T = 20.1 seconds