Try this advanced sample GMAT problem-solving question focusing on rates. Remember, as complicated as the problems get, the key is using the distance = rate x time formula for all of the specific distances travelled.

**Problem:**

Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine’s house and Shannon’s house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rides her bike home at the rate of R miles per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does Maxine live from work?

A) 15

B) 20

C) 30

D) 40

E) 45

**Solution:**

To solve for the distance between Maxine’s house and the building in which she works, we must first translate our question into a series of equations. Remember that for each leg of a journey, we can use the distance = rate x time relationship. First, we know that the distance between Maxine and Shannon’s houses is 60 miles. If we call the distance between Maxine’s house & work D_{M, }and the distance between Shannon’s house and work D_{s}, we can write the equation D_{M} + D_{S} = 60. We can also write equations for the three types of trips. For Shannon’s drive, we can say that D_{S} = 2RT. For Maxine’s drive, we can say that D_{M} = 2R(T + 2/3) – Shannon’s time, which is T, plus 2/3 of an hour. For Maxine’s bike ride, we can say D_{M} = R(T + 2). From these equations we can solve for D_{M}.

D_{M} = R(T + 2) and D_{M} = 2R(T + 2/3), so R(T + 2) = 2R(T + 2/3). This can be simplified to RT + 2R = 2RT + 4R/3, which in turn becomes 3RT + 6R = 6RT + 4R. We can then simplify even further to say 3RT = 2R, 3T = 2, T = 2/3. Therefore, we know that it takes Shannon 2/3 of an hour to drive home.

Next, we can use the fact that D_{s }= 60 – D_{M}. This can be substituted into the equation D_{s} = 2RT, giving us 60 – D_{m} = 2RT. Because we know that T = 2/3, we know that 60 = D_{M} + 2(2/3)R. We also know that D_{M} = R(T + 2). Again keeping in mind that T = 2/3, we can substitute and say that 60 = R(2/3 + 2) + 2(2/3)R. We then solve for R:

60 = R(2/3 + 2) + 2(2/3)R

60 = 2R/3 + 2R + 4R/3

180 = 2R + 6R + 4R

180 = 12R

R = 15.

Once we know R is 15, we can plug back into the equation D_{M} = R(T + 2), which becomes D_{M }= 15(2/3 + 2) = 10 + 30 = 40. Therefore, choice **(D)** is the correct answer.

Bret has been teaching for Kaplan since 2005, and has helped over 1000 students with their GMAT preparation. He spent three years teaching in Manhattan, where he served as an Elite Teacher and a full-time instructor, before moving to London, where he is now the GMAT Master Teacher for Kaplan’s London Center. As the GMAT Master Teacher, Bret trains, observes and mentors teachers, in addition to continuing his own teaching and tutoring, and has taught courses across Europe, including Italy, Ireland, and Germany. Bret contributes to Kaplan’s GMAT curriculum on an on-going basis, and was also a contributor to Kaplan's 2010 GMAT course.