Responsibility

Sending a text message is a quick way of delivering a small bit of information or making a request.  When a request is made, a problem is described and responsibility for that problem is being discussed.  For example, consider the couple Amy and George discussing picking up their son, Johnny from school. Amy texts George, "I can't make it, so will you please remember to get Johnny from school today."  In this case, the problem being discussed is Amy can no longer make the pick-up.  The responsibility seems to shift to George.

But the shift isn't exactly automatic.  George could easily reply with "Got it honey, I'll get them home by 4:00."  But George could also just not respond.  George could think, hypothetically, "I'm not sure I can get off work by then, maybe I should see if Henry's parents can get him."  George could choose to work on that issue without telling Amy.  In this case, since no one has promised to pick up Johnny, both parents are now quasi-responsible.  

The reality of the situation is that quasi-responsible is tantamount to responsible.  Because the communication is incomplete, both Amy and George are now responsible for finding a pick-up solution.

In general, if a boss gives an employee a problem to solve, that problem is made into two problems unless the employee can actually assume responsibility for the problem.  "I heard you. I'm on it. You can trust me on this."  It's not efficient for the boss to still be responsible and have to look over the employee's shoulder all the time.

When receiving a text message, answer it immediately.  If you choose to delay answering, instead of solving a problem, you now have two problems: both of you are now responsible.