Sally can detail a car in 50 minutes. manny does the same job in 35 minutes. how long will it take them to detail a car working together

Both Sally ans Manny can detail a car in 20.6 min.

Solution:

Let us assume that together they will take total x minutes to detail the car.

Sally detail the car in 50 min.

So in 1 min sally can detail \left(\frac{1}{50}\right) of the car.

Hence in x min sally can detail \left(\frac{x}{50}\right) of the car.

Manny can detail a car in 35 min.

So in 1 min many can detail \left(\frac{1}{35}\right) of the car.

Hence in x min Manny can detail \left(\frac{x}{35}\right) of the car.

So we can say,

\left(\frac{x}{50}\right)+\left(\frac{x}{35}\right)=1

x\left(\frac{1}{50}+\frac{1}{35}\right)=1

x\left(\frac{7+10}{350}\right)=1

\left(\frac{17 x}{350}\right)=1

x=\left(\frac{350}{17}\right)=20.5 8 20.6

So, both of them can detail a car in 20.6 min.