The PTA placed a trail marker in the ground every four hundreds yard. What is the shortest distance a runner will have to run to see both a water station and trail marker at the same location

At 3600 yard both will be at the same distance.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

The PTA placed a trail marker in the ground every four hundred yards. Every nine 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 a trail marker at the same location?

Since trail marker has been installed in the ground at every 400 yards so the sequence for the trail marker will be

400, 800, 1200, 1600, ...

At every 900 yards PTA set up a water station so the sequence will be,

900, 1800, 2700, 3600, ...

Now we have to find the shortest distance at which runner will see both will be the common term of both the sequences (arithmetic) formed.

So the shortest distance at which both will meet, will be LCM of 400 and 900.

LCM of 400 and 900 = 3600

Therefore, at 3600 yards both will be at the same distance.