The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground....
GMAT Algebra : (Alg) Questions
The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height \(\mathrm{h}\), in feet, of the front of the roller-coaster car \(\mathrm{s}\) seconds after it starts up the hill?
1. TRANSLATE the problem information
- Given information:
- Initial height: 15 feet above ground
- Rate of rise: 8 feet per second
- Need to find: height h after s seconds
2. INFER the mathematical relationship
- This describes linear motion with constant rate
- Linear equations have the form: \(\mathrm{Final~Value = Rate \times Time + Initial~Value}\)
- For height: \(\mathrm{h = (rate~of~change) \times (time) + (starting~height)}\)
3. INFER the correct equation structure
- Rate of change = 8 feet per second → coefficient of s
- Initial height = 15 feet → constant term
- Therefore: \(\mathrm{h = 8s + 15}\)
Answer: A. \(\mathrm{h = 8s + 15}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students mix up which number represents the rate versus the initial condition.
They might think: "15 is bigger, so it must be the rate" or "8 comes first in the problem, so it goes first in the equation." This leads them to write \(\mathrm{h = 15s + 8}\), where they've switched the coefficient and constant.
This leads them to select Choice D (\(\mathrm{h = 15s + 8}\)).
The Bottom Line:
Success requires clearly distinguishing between initial conditions (which become constants) and rates of change (which become coefficients). The structure of linear equations directly reflects the physical situation: you start somewhere and change at a constant rate over time.