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.

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" GMAT-Club-Forum-uwlgcmts.png

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% .