ANSWER:
Sally and Manny together can detail a car in 20 minutes 59 seconds
SOLUTION:
Given,
Sally can detail a car in 50 minutes
Work done by sally in one minute = [tex]\frac{1}{50}[/tex]
Manny does the same job in 35 minutes
Work done by Manny in one minute = [tex]\frac{1}{35}[/tex]
Now, work done by Sally and Manny together in one minute = [tex]\frac{1}{50}+\frac{1}{35}[/tex]
[tex]=\frac{1}{5}\left(\frac{1}{10}+\frac{1}{7}\right)[/tex]
[tex]=\frac{1}{5}\left(\frac{7+10}{7 \times 10}\right)[/tex]
[tex]=\frac{1}{5} \times \frac{17}{70}[/tex]
[tex]=\frac{17}{350}[/tex]
So, the time taken to detail a car by sally and manny together is [tex]\frac{350}{17}=20.5882[/tex]
Hence, sally and manny together can detail a car in 20 minutes 59 seconds or 23 minutes(approximately)
