We can define a rate as the quotient between two variables.
With this we will find:
a) 7.14 hours
b) 168 potatoes.
Knowing that Sam takes 4 hours to peel 32 potatoes, the rate at which he peels potatoes is:
S = (32 potatoes)/(4 hours) = 8 potatoes per hour.
And we know that Josh needs 5 hours to peel 30 potatoes, then Josh's rate is:
J = (30 potatoes)/(5 hours) = 6 potatoes per hour.
a) If Josh and Sam work together, then the rate at wich they work is:
(S + J)
And we want to find the time T such that they peel 100 potatoes.
Then we need to solve for T:
(S + J)*T = 100 potatoes
(8 potatoes per hour + 6 potatoes per hour)*T = 100 potatoes
(14 potatoes per hour)*T = 100
T = 100/(14 potatoes per hour) = 7.14 hours
So they need 7.14 hours to peel 100 potatoes.
b) Here we just need to compute:
(S + J)*12 hours
(14 potatoes per hour)*12 hours = 168 potatoes.
If you want to learn more, you can read:
https://brainly.com/question/24542879
