Answer:
45
Step-by-step explanation:
These work problems are always done in terms of fractions ie if both (Kevin & Eric) took 30mins to mow and Kevin took 1.5hrs (90mins) alone then we can make an equation like below
1/time took for both = 1/time took for Kevin + 1/time took for Eric
1/30 = 1/90+1/x ==> calling time took for Kevin x
solving the above 1/x = 1/30-1/90
1/x=2/90
x=45
Given that Kevin takes 1.5 hours to mow the lawn alone and together
with Eric it takes 30 minutes The time it takes Eric alone is 45 minutes.
The time it takes Kevin to mow the lawn, K = 1.5 hours
The time it takes Kevin and Eric to mow the lawn, B = 30 minutes = 0.5 hours
Required:
The time it takes Eric to mow the lawn alone.
Solution:
Let K represent the time it takes Kevin to mow the lawn alone and let E
represent the time it takes Eric to mow the lawn alone, we have;
[tex]\mathbf{\dfrac{1}{K} + \dfrac{1}{E} }= \dfrac{1}{T}[/tex]
Which gives;
[tex]\dfrac{1}{1.5} + \dfrac{1}{E} = \dfrac{1}{0.5}[/tex]
Which gives;
[tex]\dfrac{1}{E} = \dfrac{1}{0.5} - \dfrac{1}{1.5} =\dfrac{4}{3}[/tex]
Therefore;
[tex]E = \dfrac{1}{\dfrac{4}{3} } = \dfrac{3}{4} = \mathbf{ 0.75}[/tex]
The time it takes Eric to mow the lawn alone, E = 0.75 hours
0.75 hours = 0.75 × 60 minutes = 45 minutes
The time it takes Eric to mow the lawn alone, E = 45 minutes
Learn more about proportions here:
https://brainly.com/question/15638750
