Fingernails grow at an average of #"0.5 mm"# per week. How long will it take fingernails to reach #"10 cm"# and #"1 m"# in length?

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Answer 1 · 2017-11-16T04:29:30

It will take about 200 weeks for fingernails to reach 10 cm (100 mm), and 2000 weeks to reach 1 m (1000 mm).

Given:

#"0.5 mm = 1 week"#

Time to reach 10 cm (100 mm).

Conversion of #"cm"# to #"mm"#.

#"1 cm = 10 mm"#

Convert #"10 cm"# to #"mm"#.

#10color(red)cancel(color(black)("cm"))xx(10"mm")/(1color(red)cancel(color(black)("cm")))="100 mm"#

Multiply #"mm"# by #"1 week"/"0.5 mm"#.

#100color(red)cancel(color(black)("mm"))xx(1"week")/(0.5color(red)cancel(color(black)("mm")))="200 weeks"#

Time to reach 1 m (1000 mm).

Conversion of #"m"# to #"mm"#.

#"1 m = 1000 mm"#

Multiply #"mm"# by #(1"week")/(0.5"mm")#.

#1000color(red)cancel(color(black)("mm"))xx(1"week")/(0.5color(red)cancel(color(black)("mm")))="2000 weeks"#