1. 10 cm/sec 2. 150 cm 3. 37.4 sec

  1. Suppose speed on carpet = v cm/sec
     So speed on floor = 1.25 v
     So 200/1.25v + 400/v = 56
     Solving,  v = 10
   
  2. This question is easy for anyone who realises that it
     is analogous to the well-known problem in optics of
     a ray of light emerging from a block of glass whose
     refractive index is 1.25. Angle ECF is equal to the
     critical angle, so its sine is 1/1.25 = 0.8, and ECF
     is a 3-4-5 triangle with sides 90, 120 and 150 cm.
       
  3. CF = 150 cm and FD = 400 - 120 = 280 cm.
       So time = 150/10 + 280/12.5 = 37.4 sec

2. A listener cannot separate the sound of the two bells unless the interval between their strokes is more than 0.05 seconds. How many seconds after noon will the two bells next appear to sound together again?

3. Three bells are tolling at intervals of 1.95 seconds, 2.15 seconds, and 2.20 seconds respectively. If all three bells strike at noon, after how long will they all strike again exactly together?