Question

Washing his dad's car alone, Spencer takes 5.5 hours. If his dad helps him, then it takes 1.5 hours. How long does it take Spencer's dad to wash the car by himself??

Answer 1

20/33

Explanation:

Let's denote the rate at which Spencer works alone as S (in cars per hour) and the rate at which his dad works alone as D.

When Spencer works alone, he takes 5.5 hours, so the work rate equation is 5.5S=1 (since they complete one car).

When Spencer and his dad work together, they take 1.5 hours, so the work rate equation is 1.5(S+D)=1.

Now, we have a system of two equations:

5.5S=1

1.5(S+D)=1

First, solve the first equation for S:

S=1/5.5

Now, substitute this expression for S into the second equation:

1.5((1/5.5)+D)=1

Solve for D:

1.5((1/5.5)+D)=1

(1/5.5)+D=2/3

D=(2/3)-(1/5.5)

Now, find a common denominator:

D= (2⋅5.5−1)/(3⋅5.5)

D= (11-1)/16.5

​D= 10/16.5

​

Now, simplify:

D= 20/33

​So, Spencer's dad, working alone, takes 20/33 hours to wash the car by himself.