Chapter 11.5, Problem 4LC

To determine

How long it will take for both them to pick a bushel together.

Answer to Problem 4LC

  $\frac{225}{8}=28.125\text{ minutes}$

Explanation of Solution

Given:

S pics a bushel of apples in 45 min and A pics a bushel of apples in 75 min.

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
1. Multiply both sides of equations by LCD(least common denominator) of all denominators.
2. Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In order tofind the time it will take for both them to pick a bushel together, observe that S can picks a bushel of apples in 45 min, so in 1 minute she can pick $\frac{1}{45}$ th part of the bushel. And Acan picks a bushel of apples in 75 min, so in 1 minute he can pick $\frac{1}{75}$ th part of the bushel.

Now if they both picks a bushel together, in 1 minute they both can pick

  $\begin{array}{c}\frac{1}{45}+\frac{1}{75}=\frac{1}{45}\cdot \frac{5}{5}+\frac{1}{75}\cdot \frac{3}{3}\\ =\frac{5}{225}+\frac{3}{225}\\ =\frac{5+3}{225}\\ =\frac{8}{225}\end{array}$

So, they together can pick a bushel of apple in $\frac{225}{8}=28.125$ minutes.

Thus, it will take $\frac{225}{8}=28.125$ minutes for both them to pick a bushel of apple together.