1. ## Lawnmower Problem

The Smith family has two lawnmowers, one old and one new. Here is a table for how long it takes each son to mow the lawn using each lawnmower and working alone.

New Old
Johnny 2 hrs 2 hrs 30 min
Jimmy 3 hrs 3 hrs 40 min

How long does it take them working together:
a. If Johnny uses the new one and Jimmy uses the old one?

b. If Johnny uses the old one and Jimmy uses the new one?

Thanks,

Steve

2. Originally Posted by skweres1
The Smith family has two lawnmowers, one old and one new. Here is a table for how long it takes each son to mow the lawn using each lawnmower and working alone.

New Old
Johnny 2 hrs 2 hrs 30 min
Jimmy 3 hrs 3 hrs 40 min

How long does it take them working together:
a. If Johnny uses the new one and Jimmy uses the old one?

b. If Johnny uses the old one and Jimmy uses the new one?

Thanks,

Steve
Johnny's rates ... $\displaystyle \frac{1 \, job}{2 \, hrs}$ and $\displaystyle \frac{1 \, job}{(5/2) \, hrs}$ or $\displaystyle \frac{2 \, jobs}{5 \, hrs}$

Jimmy's rates ... $\displaystyle \frac{1 \, job}{3 \, hrs}$ and $\displaystyle \frac{1 \, job}{(11/3) \, hrs}$ or $\displaystyle \frac{3 \, jobs}{11 \, hrs}$

Jonny new , Jimmy old working together ...

$\displaystyle \left(\frac{1 \, job}{2 \, hrs} + \frac{3 \, jobs}{11 \, hrs} \right)(t \, hrs) = 1 \, job \, done$

solve for t

3. Hello, Steve!

The Smith family has two lawnmowers, one old and one new.
Here is a table for how long it takes each son to mow the lawn using each lawnmower and working alone.

$\displaystyle \begin{array}{c||c|c|} & \text{New} & \text{Old } \\ \hline \hline \text{Johnny} & \text{2 hrs} & \text{2 hrs, 30 min} \\ \hline \text{Jimmy} & \text{3 hrs} & \text{3 hrs, 40 min} \\ \hline \end{array}$

How long does it take them working together:

(a) If Johnny uses the new one and Jimmy uses the old one?

(b) If Johnny uses the old one and Jimmy uses the new one?

(a) Using the new mower, Johnny takes mows the lawn in 2 hours
. . In one hour, he mows $\displaystyle \tfrac{1}{2}$ of the lawn.
. . In $\displaystyle x$ hours, he mows $\displaystyle \frac{x}{2}$ of the lawn.

Using the old mower, Jimmy takes $\displaystyle 3\tfrac{2}{3} = \tfrac{11}{3}$ hours.
. . In one hour, he mows $\displaystyle \frac{1}{\frac{11}{3}} = \tfrac{3}{11}$ of the lawn.
. . In $\displaystyle x$ hours, he mows $\displaystyle \frac{3x}{11}$ of the lawn.

Working together, in $\displaystyle x$ hours, they can mow: .$\displaystyle \frac{x}{2} + \frac{3x}{11} \,=\,\frac{17x}{22}$ of the lawn.

But in $\displaystyle x$ hours, we expect to mow the entire lawn (1 lawn).

There is our equation: .$\displaystyle \frac{17x}{22} \:=\:1 \quad\Rightarrow\quad x \:=\:\frac{22}{17}$

Working together, they can mow the law in $\displaystyle 1\tfrac{5}{17}$ hours.

Use the same procedure for part (b).