Chapter 12.6, Problem 11P

To determine

To find:time taken by each person to pick the bushel of apples alone.

Answer to Problem 11P

The time taken by Johannes was $6\min$ and time taken by Maria was $10\min$ to pick bushel of apples alone.

Explanation of Solution

Given information:

Maria took $4\min$ more than Johannes to pick bushel of apples and together they took $16\min$ to pick bushel of apples.

Formula:

We will equate the variables to the left hand side and constant to the right hand side.

Calculation:

Consider that the Johannes took $x\min$ to pick the bushel of apple.

As mentioned above Maria took $4\min$ more than Johannes to pick bushel of apples.

Therefore Maria took $\left(x+4\right)\min$ to pick bushel of apples alone.

When they worked together they both took $16\min$ to pick bushel of apples.

Therefore $x+\left(x+4\right)=16$ .

Recall that we will equate the variables to the left hand side and constant to the right hand side.

Therefore $x+\left(x+4\right)=16\Rightarrow 2x+4=16\Rightarrow 2x=12\Rightarrow x=6$ .

Therefore the Johannes took $6\min$ to pick the bushel of apples and Maria took $\left(x+4\right)\min \Rightarrow 6+4=10\min$ to pick bushel of apples alone.