Question

A caterpillar climbs up a one-meter wall. For every 2 cm it climbs up, it slides down 1 cm. It takes 10 minutes for the caterpillar to climb to the top. Calculate the speed at which the caterpillar travels in cm/s.

Answer 1

After 1 move, it reaches 2cm but ends up at 1 cm.
After 2 moves, it reaches 3cm but ends up at 2 cm.
After 3 moves, it reaches 4cm but ends up at 3 cm.
After 4 moves, it reaches 5cm but ends up at 4 cm.
After 5 moves, it reaches 6cm but ends up at 5 cm.
.
.
.
After 96 moves, it reaches 97cm but ends up at 96 cm.
After 97 moves, it reaches 98 cm but ends up at 97 cm.
After 98 moves, it reaches 99 cm but ends up at 98 cm.
Then, on the 99th move, it climbs up 2 cm, to 100 cm.

The critter has just momentarily reached the 100-cm point
after climbing 99 times.

If the sliding takes no time, then

   Speed = (total distance climbed) / (total time)

               = (99 x 2 cm)  /  (10 minutes)

               =  (198 cm) / (600 sec)

               =    0.33 cm/sec

Answer 2

If the caterpillar goes up 2cm then slips down 1cm, it only got 1 cm
The poor caterpillar had to crawl 3m to get up 1m .

average speed = distance travelled / time taken
average speed = 3m / 10 minutes
average speed = 0.33 m / minutes

or
average speed = (9 x 2 cm)  /  (10 minutes)
average speed =  (198 cm) / (600 sec)
average speed =    0.33 cm/sec