The problem. Click for her solution.

In June 2014, Parade Magazine featured columnist Marilyn vos Savant  presented a classic work problem. Then she described her solution–which was totally wrong (Link to solution). Apparently I wasn’t the only one to catch her error.

Several weeks later, she posted a “correction”. Unfortunately, she still failed to clearly present the solution. This was a classic first year algebra problem. Unlike many problems that are set up to have rather easy answers, this one could only be solved by using the quadratic equation.

The Correct Solution

Marilyn’s approach goes wrong when she states that they work “12 man hours” based on 2 people working a total of 6 hrs. Brad and Angelina don’t work at the same rate!

Work done =(rate of work) x (time worked)
You can make 2 equations:
Say Brad works at the rate of “B” projects per hour,
and Angie works “A” projects/hr. so:
6A + 6B = 1 (working together to complete one project)

Separately, Angie takes “t” to complete, and Brad takes (t+4). Their rates are A=1/t and B=1/(t+4), so the first equation can be re-written as:
6 (1/t) + 6 (1/t+4) = 1
Now you solve for t (t^2 is “t squared”):
t^2-8t-24=0
Use the quadratic equation, and you get:
t=10.32 hours for Angeline; t+4=14.32 hours for Brad

Marilyn’s Correction

Click for larger image.

This was her followup attempt to correct the first wrong answer. I think it’s very poorly done!

Based on her murky “correction”, I posted the following comments on her website (http://parade.condenast.com/308009/marilynvossavant/308009/#comments)

Marilyn’s “correction” (7/13 issue) was very disappointing and weak. It could have been a teachable moment:
1. Always check your answers before publishing.
2. Some problems require rigorous, methodical math to solve, and there are not always “tricks” that you can use to avoid such math.
3. Math is powerful and you don’t need to be a genius to learn it.
4. Algebra is a more powerful tool than arithmetic.
5. Explain what a man-hour really means (she clearly didn’t understand this, nor admit that she didn’t).
6. Ask other people to check your work with a “fresh set of eyes.”

Instead of showing the actual solution, she makes this statement that really doesn’t help much:
“I didn’t notice that when they work apart, the advantage of her speed is limited to only half of the work.” WHAT? HUH??

This is first year algebra, and though many (most?) readers might not understand it, the real solution should have been posted–not just “10.32 hrs. That would have been a great illustration for math teachers to show their students that they can do something the “genius lady” couldn’t do.