Question

A monkey is swinging from a tree. On each swing, she travels along an arc that is

75%, percent as long as the previous swing's arc. The total length of the arcs from her first 4 swings is 175m.How long was the monkey's 1st swing?
Round your final answer to the nearest meter.

Answer 1

Total length of the first swing=64 m

Explanation:

The total length of all four swings can be expressed as; Total length of all 4 swings=Length of first swing+length of second swing+length of third swing+length of fourth swing

where;

Total length of all 4 swings=175 m

Length of first swing=x

Length of second swing=75% of length of first swing=(75/100)×x=0.75 x

Length of third swing=75% of length of second swing

Length of third swing=(75/100)×0.75 x=0.5625 x

Length of fourth swing=75% of length of third swing

Length of fourth swing=(75/100)×0.5625 x=0.421875 x

replacing;

Total length of all 4 swings

175=x+0.75 x+0.5625 x+0.421875 x

2.734375 x=175

x=175/2.734375

x=64

Total length of the first swing=x=64 m