A geophysicist uses a drone to survey an area every 15 days and a satellite to scan the same area every 20 days. If both started today, how many days will pass before both the drone survey and satellite scan occur on the same day again? - Redraw
Title: Finding the Common Rhythm: Drone and Satellite Surveys Aligned Every 60 Days
Title: Finding the Common Rhythm: Drone and Satellite Surveys Aligned Every 60 Days
When managing environmental monitoring or geological surveys, timing is everything. In a recent geophysical study, a dedicated geophysicist leveraged two powerful tools—a drone and a satellite—to collect data from the same remote site. The drone conducts detailed ground-level surveys every 15 days, while the satellite performs wide-ranging scans every 20 days. But an important question arises: When will both surveys coincide again on the same day?
The key to solving this lies in the mathematical concept of the least common multiple (LCM). By analyzing the funding intervals—15 days for drones and 20 days for satellites—we determine after how many days both devices will survey the area simultaneously.
Understanding the Context
Understanding the Intervals
- Drone survey interval: 15 days
- Satellite scan interval: 20 days
To find when both will occur again on the same day, calculate the LCM of 15 and 20.
Image Gallery
Key Insights
Calculating the Least Common Multiple
First, factor both numbers:
- 15 = 3 × 5
- 20 = 2² × 5
The LCM is found by taking the highest power of each prime factor:
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- 2² × 3 × 5 = 4 × 3 × 5 = 60
Thus, the LCM of 15 and 20 is 60.
When Will They Survey Together Again?
Since both devices began today—day 0—they will both survey the area again after 60 days. This means that every 60 days, the drone will fly over the site on a scheduled survey, and the satellite will capture a comprehensive scan, aligning perfectly for synchronized data collection.
This synchronized rhythm enhances monitoring efficiency, enabling geophysicists to cross-reference high-resolution local data with broader satellite insights at regular, predictable intervals.
Practical Applications for Geophysics
Using drones and satellites in tandem offers transformative advantages in geophysical surveys:
- Drone surveys provide precise, close-range measurements ideal for detailed terrain analysis, subsurface testing, and localized environmental changes.
- Satellite imaging offers wide-area coverage, tracking broader patterns like land deformation, vegetation shifts, or seismic activity over large regions.
