# GMAT Challenge Series (700+): Q13

Question:

A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A. 48

B. 72

C. 96

D. 120

E. 192

$$\text{Let x equal the speed of the buses}$$ $$\text{Let 2P equal distance between M and N, with P being the midpoint}$$  $$\text{Day 1:}$$ $$\text{M ---------------------------> P <--------------------------- N}$$ $$\text{Day 2:}$$ $$\text{M ---------> P - 24 | P + 24 <------------------------------- N}$$  $$\textit{speed} = {\textit{distance} \over \textit{time}}$$ $$\text{Late bus:}$$ $${x} = {\text{P - 24} \over \text{1.6}}$$ $$\text{Early bus:}$$ $${x} = {\text{P + 24} \over \text{2.6}}$$ $$\text{Solve:}$$ $${\text{P - 24} \over \text{1.6}} = {\text{P + 24} \over \text{2.6}}$$ $$\text{2.6P} - {2.6}\left({24}\right) = \text{1.6P} + {1.6}\left({24}\right)$$ $$\text{P} = {4}\left({24}\right)$$ $$\text{P} = {96}$$ $$\text{2P} = {192}$$