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04 Aug 2025, 04:27
Kudos
Bookmarks
\(x\): 260
\(y\): 200
In a certain mega-shopping mall, Carla and Daniel start from the beginning of a 200-meter-long moving walkway and move in the same direction as the walkway, which travels at a constant speed of 0.5 meters per second.
• Carla starts running at a constant rate of 1 meter per second relative to the walkway, continues running for exactly 40 seconds, and then stops running for \(x\) seconds. While not running, Carla stands still and is carried only by the walkway.
• Afterward, she resumes running at 1.5 meters per second relative to the walkway for exactly 5 seconds, at which point she reaches the end of the walkway.
• Daniel walks at a constant rate of 0.5 meter per second relative to the walkway, from start to finish without stopping, and reaches the end in \(y\) seconds.
Select for x and y the value of of \(x\) and \(y\), that are consistent with the information provided. Make only two selections, one in each column.
• Carla starts running at a constant rate of 1 meter per second relative to the walkway, continues running for exactly 40 seconds, and then stops running for \(x\) seconds. While not running, Carla stands still and is carried only by the walkway.
• Afterward, she resumes running at 1.5 meters per second relative to the walkway for exactly 5 seconds, at which point she reaches the end of the walkway.
• Daniel walks at a constant rate of 0.5 meter per second relative to the walkway, from start to finish without stopping, and reaches the end in \(y\) seconds.
Select for x and y the value of of \(x\) and \(y\), that are consistent with the information provided. Make only two selections, one in each column.
| \(x\) | \(y\) | |
| 100 | ||
| 130 | ||
| 200 | ||
| 250 | ||
| 260 | ||
| 300 |
ShowHide Answer
Official Answer
\(x\): 260
\(y\): 200
04 Aug 2025, 04:27
Kudos
Bookmarks
Official Solution:
The walkway moves at a constant speed of 0.5 meters per second.
Step 1: Distance Carla runs in each phase
– In the first phase, Carla runs at 1 meter per second relative to the walkway.
Her total speed = 1 + 0.5 = 1.5 meters per second
Time = 40 seconds
Distance = 1.5 * 40 = 60 meters
– In the last phase, Carla runs at 1.5 meters per second relative to the walkway.
Her total speed = 1.5 + 0.5 = 2.0 meters per second
Time = 5 seconds
Distance = 2.0 * 5 = 10 meters
Step 2: Distance and time while Carla is stationary
Total distance = 200 meters
Distance already covered while running = 60 + 10 = 70 meters
Remaining distance = 200 - 70 = 130 meters
While standing still, she moves only with the walkway:
Speed = 0.5 meters per second
Time = 130 / 0.5 = 260 seconds
Step 3: Daniel's total time
Daniel walks at 0.5 meters per second relative to the walkway.
His total speed = 0.5 + 0.5 = 1.0 meter per second
Distance = 200 meters
Time = 200 / 1.0 = 200 seconds
Correct answer:
\(x\) "260"
\(y\) "200"
Bunuel
The walkway moves at a constant speed of 0.5 meters per second.
Step 1: Distance Carla runs in each phase
– In the first phase, Carla runs at 1 meter per second relative to the walkway.
Her total speed = 1 + 0.5 = 1.5 meters per second
Time = 40 seconds
Distance = 1.5 * 40 = 60 meters
– In the last phase, Carla runs at 1.5 meters per second relative to the walkway.
Her total speed = 1.5 + 0.5 = 2.0 meters per second
Time = 5 seconds
Distance = 2.0 * 5 = 10 meters
Step 2: Distance and time while Carla is stationary
Total distance = 200 meters
Distance already covered while running = 60 + 10 = 70 meters
Remaining distance = 200 - 70 = 130 meters
While standing still, she moves only with the walkway:
Speed = 0.5 meters per second
Time = 130 / 0.5 = 260 seconds
Step 3: Daniel's total time
Daniel walks at 0.5 meters per second relative to the walkway.
His total speed = 0.5 + 0.5 = 1.0 meter per second
Distance = 200 meters
Time = 200 / 1.0 = 200 seconds
Correct answer:
\(x\) "260"
\(y\) "200"
05 Nov 2025, 23:49
Kudos
Bookmarks
Hi
I understood the solution but I have one doubt though. Why are we adding the speeds of Carla/Daniel and the walkway? Aren't they moving in the same direction as the walkway, so by the concept of relative speed, shouldn't we subtract the speeds (Carla's Speed - Walkway's speed)? Pls help.
I understood the solution but I have one doubt though. Why are we adding the speeds of Carla/Daniel and the walkway? Aren't they moving in the same direction as the walkway, so by the concept of relative speed, shouldn't we subtract the speeds (Carla's Speed - Walkway's speed)? Pls help.
Bunuel
