Question

Watching his dad‘s car alone eight year old Levi takes 2.5 hours if his dad helps him then it takes one hour how long does it take Levi’s dad to wash the car by himself

Answer 1

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:

`=\text{ }(x)/(2.5)\text{ /hours}`

The rate at which his dad would was his car:

`=\text{ }(x)/(t)\text{ /hours}`

The rate at which both work:

`\begin{gathered} =\text{ }(x)/(1)\text{ } \\ \text{= x /hour} \end{gathered}`

The rate at which both work is equal to the rate at which Levi and his dad work individually

`\begin{gathered} x\text{ = }(x)/(2.5)\text{ +}(x)/(t) \\ x\text{ = }(xt+2.5x)/(2.5t) \\ x\text{ = }\frac{x(t\text{ + 2.5\rparen}}{2.5t} \\ (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}`

Hence, it takes Levi's dad 1 hour 40 mins