To find the number of hours, h, it takes for Joseph to catch up to Sandra, the equation 14h = 10.5h + 2.1 is used. By simplifying, we calculate h = 2.1 / 3.5, which results in h = 0.6 hours.
To find h, the number of hours it will take for Joseph to catch up to Sandra, we need to set up an equation based on the distance each of them travels on the Redstone trail. We know that distance equals speed multiplied by time. For Joseph, the distance is speed of Joseph × h, and for Sandra, the distance is speed of Sandra × h plus the head start distance.
Since Joseph is 0.5 miles from the top of the trail and Sandra is 2.6 miles from the top, Sandra has a head start of 2.6 - 0.5 = 2.1 miles. Therefore, the equation will be set up as follows:
For Joseph: Distance_Joseph = 14 × h
For Sandra: Distance_Sandra = 10.5 × h + 2.1
Joseph will catch up to Sandra when the two distances are equal, which gives us the equation:
14 × h = 10.5 × h + 2.1
To solve for h, we can subtract 10.5 × h from both sides of the equation and then divide by the difference in their speeds.
14h - 10.5h = 2.1
3.5h = 2.1
h = 2.1 / 3.5
h = 0.6