# Most US College Students Cannot Solve This Basic Math Problem. The Working Together Riddle

August 16, 2019

Hey, this is Presh Talwalkar. Alice and Bob can complete a job in two hours. Alice and Charlie can complete the same job in three hours. Bob and Charlie can complete the same job in four hours. How long will the job take if Alice, Bob, and Charlie work together? Assume each person works at a constant rate whether working alone or working with others. This problem has been asked to students in US colleges. To the professor’s surprise, many of the students set up the wrong equations and could not solve this problem. Can you figure it out? Give this problem a try and when you’re ready keep watching the video for the solution. Before I get to the solution, let me go over a common mistake in how students get to the wrong answer. They read the first sentence, that Alice and Bob can complete a job in two hours, and translate the names and the numbers into an equation. They say this must mean that A + B=2. They look at the second sentence, that Alice and Charlie can complete the job in three hours, and they similarly convert it to A + C=3. The third condition, that Bob and Charlie can complete the job in four hours, gets converted to the equation B + C=4. The question of how long it will take for all three of them working together gets translated into the question
of “what is A + B + C =?” So to solve this system of equations… They want to solve for A + B + C, so they can add up all the equations together. We end up getting two terms of A, two terms of B, and two terms of C, to equal 2 + 3 + 4. If we group the factors [summands], we get