Problems Section: Problems 1391 - 1400

Q1391 Jack looked at the clock next to his front door as he left home one afternoon to visit Jill and watch a TV programme.  Arriving exactly as the programme started, he set out for home again when it finished one hour later.  As he did so he looked at her clock and noticed that it showed the same time as his had done when he left home.  Puzzling over how Jill's clock could be so wrong, Jack travelled home at half the speed of his earlier journey.  When he arrived home he saw from his clock that the whole expedition had taken two hours and fifteen minutes.  He still hadn't worked out about Jill's clock and so he called her up on the phone.  Jill explained that her clock was actually correct (as was Jack's), but it was an ``anticlockwise clock'' on which the hands travel in the opposite direction from usual.  Jack had been in such a hurry to leave that he hadn't noticed the numbers on the clock face going the ``wrong'' way around the dial.  At what time did Jack leave home?  (Hint: see the solution of problem~1381 in this issue.)
 
Q1392 Find all real numbers $x$ which satisfy the equation
$$\lfloor x\rfloor-\{2x\}+\lceil3x\rceil=5\ .$$
As in problem 1384 we write $\lfloor x\rfloor$ for $x$ rounded to the integer below, and $\lceil x\rceil$ for $x$ rounded to the integer above; also, $\{x\}$ denotes rounding to the nearest integer, with halves rounding upwards.  For example,
$$\{\pi\}=3\quad\hbox{and}\quad \{3{\textstyle\frac12}\}=4\ .$$