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30 Nov 2024, 07:27
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Route 2 Reduction (%): 20%
Speed Increase (%): 25%
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (02:21) correct
20%
(02:09)
wrong
based on 355
sessions
History
Date
Time
Result
Not Attempted Yet
Donald takes a walk through a rainforest along Route 1, traveling at a constant speed and completing it in 5 hours. The next day, he wants to finish the walk in 4 hours. To achieve this, he has two options: take a shorter route, Route 2, and walk it at the same speed as the first day, or increase his speed on Route 1 to complete it in 4 hours.
Select for Route 2 Reduction (%) the percentage by which Route 2 should be shorter than Route 1 to complete it in 4 hours at the first-day speed, and for Speed Increase (%) the percentage by which the speed should be increased on Route 1 to ensure the walk is finished in 4 hours.
Select for Route 2 Reduction (%) the percentage by which Route 2 should be shorter than Route 1 to complete it in 4 hours at the first-day speed, and for Speed Increase (%) the percentage by which the speed should be increased on Route 1 to ensure the walk is finished in 4 hours.
| Route 2 Reduction (%) | Speed Increase (%) | |
| 10% | ||
| 16.67% | ||
| 20% | ||
| 25% | ||
| 33% | ||
| 80* |
ShowHide Answer
Official Answer
Route 2 Reduction (%): 20%
Speed Increase (%): 25%
01 Dec 2024, 18:30
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Bunuel
Official Solution:
Time * Speed = Distance.
If you reduce the time from 5 hours to 4 hours, you are essentially traveling only 4/5, or 80%, of the time traveled the previous day. This means you would cover only 80% of the distance. Therefore, Route 2 should be 20% shorter than Route 1 to complete it in 4 hours at the first-day speed.
If you reduce the time from 5 hours to 4 hours, so if you multiply the time by 4/5 but still want to cover the same distance, you need to balance this change by increasing the speed. To do so, the speed must be multiplied by 5/4, which equals 1.25. This corresponds to a 25% increase in speed, ensuring the same distance is covered in less time.
Correct answer:
Route 2 Reduction (%) "20"
Speed Increase (%) "25"
Attachment:
GMAT-Club-Forum-uwlgcmts.png [ 16.58 KiB | Viewed 1428 times ]
General Discussion
30 Nov 2024, 17:02
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1. Let the distances of routes 1 and 2 be \(L_1\) and \(L_2\), respectively.
2. Find the percentage by which Route 2 should be shorter than Route 1 to complete it in 4 hours at the first-day speed. The first-day speed was \(\frac{L_1}{5}\). Then, \(L_2 = time * speed = 4 * \frac{L_1}{5}\). The percentage that we're looking for is equal to: \(\frac{L_1 - L_2}{L_1} * 100\% = \frac{L_1 - 4 * \frac{L_1}{5}}{L_1} * 100\% = 0.2 * 100\% = 20\%\).
3. Find the percentage by which the speed should be increased on Route 1 to ensure the walk is finished in 4 hours. The increased speed has to be \(\frac{L_1}{4}\). Then, the percentage that we're looking for is equal to: \(\frac{\frac{L_1}{4} - \frac{L_1}{5}}{\frac{L_1}{5}} * 100\% = \frac{\frac{1}{20}}{\frac{1}{5}} * 100\% = 0.25 * 100\% = 25\%\).
4. Our answer will be: Route 2 Reduction (%) - 20% and Speed Increase (%) - 25%.
2. Find the percentage by which Route 2 should be shorter than Route 1 to complete it in 4 hours at the first-day speed. The first-day speed was \(\frac{L_1}{5}\). Then, \(L_2 = time * speed = 4 * \frac{L_1}{5}\). The percentage that we're looking for is equal to: \(\frac{L_1 - L_2}{L_1} * 100\% = \frac{L_1 - 4 * \frac{L_1}{5}}{L_1} * 100\% = 0.2 * 100\% = 20\%\).
3. Find the percentage by which the speed should be increased on Route 1 to ensure the walk is finished in 4 hours. The increased speed has to be \(\frac{L_1}{4}\). Then, the percentage that we're looking for is equal to: \(\frac{\frac{L_1}{4} - \frac{L_1}{5}}{\frac{L_1}{5}} * 100\% = \frac{\frac{1}{20}}{\frac{1}{5}} * 100\% = 0.25 * 100\% = 25\%\).
4. Our answer will be: Route 2 Reduction (%) - 20% and Speed Increase (%) - 25%.
