Work rate problems can trip up the most experienced test-takers, even those that are normally skilled in GMAT math. Today we’re going to try out a practice problem, and hopefully make work rate problems a little more clear.
Katie and Tony have a business making custom desks. Katie can make one desk in 4 days. Tony can make the same desk in 6 days. If the both work together and independently, how long will it take them to make 15 desks?
(A) 25 days
(B) 30 days
(C) 36 days
(D) 48 days
(E) 70 days
There are essentially two ways to solve a work problem, though we at Prep4GMAT find the first method to be far simpler.
One way to solve a work problem is to use the work/rate formula, which is T = (AB) / (A+B)
T = The time it takes for both individuals working together and independently to finish the project
A = The amount of time it takes person A to finish the project
B = The amount of time it takes person B to finish the project.
In essence, if person A can finish something in A hours and person B can finish the work in B hours, then both of them together can finish that work in (AB)/(A+B) hours.
For this particular problem, we know that Kate can finish 1 desk in 4 days and Tony can finish 1 desk in 6 days.
So we can plug those numbers into our formula
T = (AB) / (A+B)
T = (6*4)/(6+4)
T = (24)/(10)
T= 2.4 days
So if Katie and Tony work together, they can complete one desk in 2.4 days.
However, the original problem asked how long it would take the two of them to build 15 desks. So we multiply 2.4 days by 15 for a total of 36 days.
The correct answer is C.
The longer method is to use the Amount = Rate * Time formula.
A = the amount of work needed to be done, the number of houses to be painted, number of desks to be built, etc.
R= the number of miles driven per hour, the number of desks that can be built in a day, or the number of lawns moved per hour, etc.
T = Time is simply the number of hours, the number of days, etc.
We first need to find out each person’s individual rate, and then add both rates to find their rate when working together. When she works alone, Katie’s rate is 1 desk in 4 days. In other words, she can complete a 1/4th of a desk in one day. When Tony works alone, his rate is 1 desk in 6 days. So he can complete 1/6th of a desk in one day.
So R = 1/6 +1/4 R = 2/12 + 3/12 R = 5/12
So Katie and Tony can complete 5/12 of a desk each day when they work together.
Returning to the A=RT formula, we can plug in 5/12 for R and 15 for A.
We need to find “T,” the amount of time it will take Katie and Tony to build these 15 desks if they’re working at a rate of 5/12 desks per day.
15 = (5/12)(T)
15/(5/12) = 15
In order to divide 15 by 5/12, we can switch the numerator and denominator of the fraction and then multiply the new fraction by 15. 15 / (5/12) = 15 * (12/5).
(15/5)*12 = 3*12 = 36
So it would take 36 days for Katie and Tony to build 15 custom desks.
The correct answer is C.
Most people find the first method easier, but with enough work problem practice questions, you will find a method that works best for you.
Feel free to chime in with your own tips and strategies in the comment section. For more practice on problem solving or data sufficiency questions, download Prep4GMAT for free and practice thousands of authentic GMAT questions with detailed explanations.