The PTA placed a trail marker in the ground every five hundred yards. Every eight hundred yards the PTA set up a water station. What is the shortest distance a runner will have to run to see both a water station and trail marker at the same location?

3600.

Step-by-step explanation:

There will be a trail marker at the following distances from the start of the trail.

400,800,1200,1600,2000,2400,2800,3200,3600,4200 and beyond

There will be water stations at the following distances from the start of the trail.

900,1800,2700,3600,4500 and beyond.

The first time that there will be a trail marker and a water station at the same point will be 3600, that is the first multiple of 400 and 900.

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