Number and Math Play

Clockwork

Three clocks in the train station give the following readings:

CLOCK A:   8:00 CLOCK B:   8:50 CLOCK C:   8:20

One clock is 20 minutes fast. One clock is slow. One clock is off by half an hour.

Help the passengers figure out what time it really is.

The time is 8:30. To get the answer, make a chart listing all the possibilities:

 20 MIN. FAST SLOW OFF BY 1/2 HOUR 8:00 (real time 7:40) 8:50 (no good--would be fast) 8:20 (no good--real time would have to be 7:50 or 8:50) 8:00 (real time is 7:40) 8:20 (no good--would be fast) 8:50 (no good--real time would have to be 8:20 or 9:20) 8:50 (real time is 8:30) 8:00 (ok-would be slow) 8:20 (no good--real time would have to be 7:50 or 8:50) 8:50 (real time is 8:30) 8:20 (ok-would be slow) 8:00 (ok--real time would have to be 7:30 or 8:30) 8:20 (real time is 8:00) 8:00 (ok-would be slow) 8:50 (no good--real time would have to be 8:20 or 9:20) 8:20 (real time is 8:00) 8:50 (no good-would be fast) 8:00 (no good--real time would have to be 7:30 or 8:30)

The fourth row in the chart is the only one in which all the information given in the puzzle can be true.