Final answer:
The equation 5s + 100 = 3s + 150 would determine the time it takes for the red balloon to catch up with the orange balloon, assuming the red balloon rises at 5 feet per second from 100 feet off the ground.
Step-by-step explanation:
To determine the amount of time required for the red balloon to catch up with the orange balloon, which is 150 feet off the ground and rising at a rate of 3 feet per second, we must assume that the red balloon starts at ground level and rises at a different rate. Without the rate at which the red balloon is rising, we cannot determine which equation is accurate. However, generally, the equation would be set up by equalizing the distances traveled by both balloons over time. For example, if the red balloon rises at 5 feet per second, the equation would be 5s + 100 = 3s + 150, where 's' represents the number of seconds after the red balloon has started its ascent. Solving this equation would give us the amount of time 's' for the red balloon to reach the same altitude as the orange balloon.
The starting position of the red balloon (100 feet presumably) is represented by the constant term. The '3s' term represents the orange balloon's ongoing ascent. Both balloons' positions as functions of time are set equal to each other to find the moment in time when their altitudes are the same, meaning the red balloon has caught up.