To solve this question we have to find the rate of each one
∵ Jane can detail a car in 35 minutes
∴ Her rate = 1/35
∵ Sally can do the same job in 40 minutes
∴ Her rate = 1/40
∵ They are working together to do the same rate
Assume that they will work for t minutes, then
[tex]\therefore\frac{1}{35}\times t+\frac{1}{40}\times t=1[/tex]Now we will add the 2 fractions
[tex]\begin{gathered} \because\frac{1}{35}t+\frac{1}{40}t=1 \\ \therefore\frac{1(40)t+1(35)t}{(35)(40)}=1 \\ \therefore\frac{40t+35t}{1400}=1 \\ \therefore\frac{75t}{1400}=1 \end{gathered}[/tex]By using cross multiplication
[tex]\therefore75t=1400[/tex]Divide both sides by 75
[tex]\begin{gathered} \because\frac{75t}{75}=\frac{1400}{75} \\ \therefore t=\frac{56}{3} \end{gathered}[/tex]They will take 56/3 minutes t finish the job together
You can write it as a mixed number 18 2/3 minutes
