Multiple choice

A cyclist traveled a certain distance at a constant speed. If the speed had been increased by 4 km per hour, the journey would have taken 1 hour less. However, if the speed had been decreased by 5 km per hour, the journey would have taken 2 hours longer. What is the total distance, in km, covered by the cyclist?

  1. 120

  2. 180

  3. 200

  4. 220

  5. a
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let d be distance and v be speed. d/v - d/(v+4) = 1 and d/(v-5) - d/v = 2. Solving these equations: d(v+4-v)/(v(v+4)) = 1 => 4d = v^2 + 4v. d(v-(v-5))/(v(v-5)) = 2 => 5d = 2v^2 - 10v. From first, d = (v^2+4v)/4. Substitute: 5(v^2+4v)/4 = 2v^2 - 10v => 5v^2 + 20v = 8v^2 - 40v => 3v^2 = 60v => v = 20. d = (400+80)/4 = 120.

AI explanation

Let the total distance be D km, the original speed be S km/hr, and the usual time be T hours; we establish the equations D = S * T, D = (S + 4) * (T - 1), and D = (S - 5) * (T + 2). Equating the first two gives S = 4T - 4, and equating the first and third gives 2S = 5T + 10. Solving this system yields T = 6 hours and S = 20 km/hr, making the total distance 120 km.

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