Lawn Activity

Question

Mrs Higgins has 3 children Jane,
Jennifer and Jessica. She wants
them to mow the lawn quickly
before her guests arrive. Since the
property is large, she has 3
mowers. Jane can mow the whole
lawn in 3 hours, Jennifer can mow
it in 2 hours and Jessica can mow
it in 4 hours. If they all work
together how long, to the nearest
second, will it take to mow the
lawn?

Answer 1

Hi Michael,

 

Fraction of lawn        Fraction of lawn       Fraction of lawn

mowed by Jane  +  mowed by Jennifer + mowed by Jessica = 1

 

Rate at which Jane work = 1/3

Rate at which Jennifer work = 1/2

Rate at which Jessica work =1/4

Let t be the time it takes the three to mow the lawn

(1/3)t + (1/2)t +(1/4)t = 1

13t/12 = 1

t = (12/13 hr)(60 minutes/1 hr) = 55.38 minutes

 

Jane, Jennifer, and Jessica will finish mowing the lawn when working together in 55 minutes 23 seconds.