AlgebraVery hardDistance from a round trip at two speeds
Algebra practice question
A cyclist rides from home to a town at 12 kilometres per hour and returns along the same road at 18 kilometres per hour. The whole trip takes 5 hours. How far, in kilometres, is the town from the cyclist's home?
Answer: 36
d/12 + d/18 = 5. With denominator 36: 3d + 2d = 180, so d = 36.
Common wrong answers
- If you answered 30
- 30 uses d/12 + d/18 = 5 with a slip, 6d = 180.
- If you answered 75
- 75 uses the average speed 15 km/h for the full 5 hours, which gives the round-trip distance, not the one-way distance.
- If you answered 37.5
- 37.5 halves 75, but averaging the two speeds is not valid when the times differ.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.