Strawberries in hanging baskets

[ilovespinach]

I'm very new to gardening. I've got two strawberry plants growing in hanging baskets on my balcony. I'm watering them often and feeding them. They're flowering but I'm disappointed that they're not producing strawberries.

I've noticed on each plant lots of dangling bits (runners?). Should I leave these or should I cut them off? I've read that the plant might be using all of it's energy growing these and not producing fruit.

If they're flowering they should bare fruit soon surely unless they've already had their first flower and nothing came of it?

It certainly looks like the start of a fruit on the flower in that photo