Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is:
Question:
Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is:
Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is:
Options
Answer: 60
Explanation:
Step 1: Define variables Let L = length of the escalator (in steps) Let M = Moody's normal walking speed (steps per second) Let E = escalator speed (steps per second) When Moody walks at his normal speed, he takes 30 seconds: L = (M + E) × 30 When Moody walks at twice his normal speed, he takes 20 seconds: L = (2M + E) × 20 Step 2: Solve for escalator speed Set the two expressions for L equal: 30(M + E) = 20(2M + E) Expand both sides: 30M + 30E = 40M + 20E Simplify: -10M + 10E = 0 → E = M So the escalator moves at the same speed as Moody's normal walking speed. Step 3: Time if Moody stands still Standing still → speed relative to ground = E = M Length of escalator L = 30(M + E) = 30 × (M + M) = 60M Time to finish standing still = L / E = 60M / M = 60 seconds Answer: 60 seconds
Explanation:
Step 1: Define variables Let L = length of the escalator (in steps) Let M = Moody's normal walking speed (steps per second) Let E = escalator speed (steps per second) When Moody walks at his normal speed, he takes 30 seconds: L = (M + E) × 30 When Moody walks at twice his normal speed, he takes 20 seconds: L = (2M + E) × 20 Step 2: Solve for escalator speed Set the two expressions for L equal: 30(M + E) = 20(2M + E) Expand both sides: 30M + 30E = 40M + 20E Simplify: -10M + 10E = 0 → E = M So the escalator moves at the same speed as Moody's normal walking speed. Step 3: Time if Moody stands still Standing still → speed relative to ground = E = M Length of escalator L = 30(M + E) = 30 × (M + M) = 60M Time to finish standing still = L / E = 60M / M = 60 seconds Answer: 60 seconds
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