1. (a)  205 km/hr forwards
      (b)  5 km/hr backwards   
   2.  2.2 sec.    
   3.  1.833.. sec

1. Locomotive moves at 100 km/sec relative to track.
   Outer edge of flange moves at 105 km/sec relative to locomotive.
     So forwards speed of A = 100 + 105 = 205 km/sec.
    And forwards speed of B = 100 - 105 = -5 km/sec.

2. Linear speed of inner race = 20 PI cm/sec.
    Consider the roller in its top position.
      Its highest point is instantaneously at rest.
      Its lowest point has speed = 20 PI cm/sec.
      So speed of centre of roller = 10 PI cm/sec.
     For one revolution, centre of roller must travel 22 PI cm.
   So time taken = 22 PI / 10 PI = 2.2 sec. 

3. Solved by a similar method.

A room measures 6m square. It has a polished floor, partially covered by a carpet 4m square, placed centrally as shown.

1. An intelligent spider, which can crawl one and a quarter times as fast on the floor as on the carpet, is on the floor at A, the mid-point of one wall, when it sees a less intelligent fly at B, the mid-point of the opposite wall. It reaches the fly in 56 seconds. How fast does it walk on carpet?

2. If the spider were at C, 90 cm from the corner of the carpet, and the fly were at D, another corner of the carpet as shown, find the length of CF, the part of its journey covered on carpet, if the spider is to reach the fly as soon as possible.

3. In this case, how long does the spider take to reach the fly?