Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 4 hours. How long does it take each of them working alone? Round your answers to the nearest tenth of an hour, if necessary.
A) Paul: $6 \mathrm{hr}$
Ron: $10 \mathrm{hr}$

B) Paul: $7.1 \mathrm{hr}$
Ron: $9.1 \mathrm{hr}$

C) Paul: $9.1 \mathrm{hr}$
Ron: $7.1 \mathrm{hr}$

D) Paul: $10 \mathrm{hr}$
Ron: $6 \mathrm{hr}$

Question

Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 4 hours. How long does it take each of them working alone? Round your answers to the nearest tenth of an hour, if necessary.
A) Paul: $6 \mathrm{hr}$
Ron: $10 \mathrm{hr}$

B) Paul: $7.1 \mathrm{hr}$
Ron: $9.1 \mathrm{hr}$

C) Paul: $9.1 \mathrm{hr}$
Ron: $7.1 \mathrm{hr}$

D) Paul: $10 \mathrm{hr}$
Ron: $6 \mathrm{hr}$

Quizplus · Accepted Answer

Let $x$ be the time it takes for Paul to mow the lawn alone. Then, Ron takes $x + 2$ hours. The rate at which Paul works is $1/x$ of the lawn per hour, and Ron's rate is $1/(x + 2)$. Together, their rate is $1/4$ of the lawn per hour since they can complete the task in 4 hours. Setting up the equation: $1/x + 1/(x + 2) = 1/4$. Solving this equation yields $x \approx 7.1$ hours for Paul and $x + 2 \approx 9.1$ hours for Ron.

Ron Can Mow the Lawn in Two Hours More Time 6hr6 \mathrm{hr}6hr

Ron Can Mow the Lawn in Two Hours More Time $6 \mathrm{hr}$