Given
It takes Levi 2.5 hours to wash his dad's car alone
It takes 1 hour if his dad helps him
Let t represent the time it takes his dad to wash his car alone
The rate at which Levi washes the car is:
[tex]=\text{ }\frac{x}{2.5}\text{ /hours}[/tex]
The rate at which his dad would was his car:
[tex]=\text{ }\frac{x}{t}\text{ /hours}[/tex]
The rate at which both work:
[tex]\begin{gathered} =\text{ }\frac{x}{1}\text{ } \\ \text{= x /hour} \end{gathered}[/tex]
The rate at which both work is equal to the rate at which Levi and his dad work individually
[tex]\begin{gathered} x\text{ = }\frac{x}{2.5}\text{ +}\frac{x}{t} \\ x\text{ = }\frac{xt+2.5x}{2.5t} \\ x\text{ = }\frac{x(t\text{ + 2.5\rparen}}{2.5t} \\ \frac{t+2.5}{2.5t}\text{ =1} \\ Cross-Multiply \\ t\text{ + 2.5 = 2.5t} \\ Collect\text{ like terms} \\ t\text{ -2.5t = -2.5} \\ -1.5t\text{ = -2.5} \\ Divide\text{ both sides by -1.5} \\ t\text{ = 1.667 hrs} \end{gathered}[/tex]
Hence, it takes Levi's dad 1 hour 40 mins
