Hilary works 1.5 times faster than sophia. if they need 5 days to mow a garden together, how long will it take sophia to mow the same garden on her own?

Question

i need help

Answer 1

Hillary takes x days

Sophia takes 1.5x days

1/x is Hillary's rate per day

1/1.5x is Sophia's rate per day

they take 5 days together

(1/x)(5)+(1/1.5x)(5)=1 (job finished)

(5/x)+(5/1.5x)=1

multiply both sides by 1.5x

(1.5)(5)+5=1.5x

7.5+5=1.5x

12.5=1.5x

125=15x

x=125/15=8 5/15=8 1/3 days for Hillary

1.5*8 1/3=1 1/2 * 8 1/3=3/2 * 25/3=25/2=12.5 days for Sophia

 

 

Answer 2

Hilary works 1.5 times faster than sophia. if they need 5 days to mow a garden together, how long will it take sophia to mow the same garden on her own?

 

So;  Say, Sophia mows the garden in X days. Then, Hilary does the job in X/1.5 days (she's faster ...)

 

In one day they, separately, do the 1/X and 1.5/X part of the job respectively.

so, in 5 days they do 5(1/X+1.5/X)=1 part [1=100% , this means they complete the job - garden is ready].

 

We must now find the X from the last equation. Simplifying ...

 

5*(1+1.5)/X=1

5*2.5/X=1

X=12.5

 

This is the answer: Sophie mows garden in 12.5 days.

 

[Hilary will mow in 12.5/1.5=8 1/3 days . They both together do it in 5 days]