Bunuel
Ship A departs dock X and heads towards dock Y at a constant speed of 10 miles per hour. 2 later, ship B departs dock X and travels along the same route at a constant speed of 14 miles per hour. Ship A does not reach dock Y before ship B. How many hours will it take for ship B to catch up with ship A?
A. 3 hrs
B. 3.5 hrs
C. 4 hrs
D. 4.5 hrs
E. 5 hrs
Three ways to approach this problem.
First, one consolidated formula.
10(t+2)=14t
10t+20=14t
20=4t
t=5
Answer choice E
Second, "pieces of the puzzle."
A travels for two hours at 10mph before B starts. A makes it 20 miles before B gets going. B gains on A at a rate of 14-10=4mph. B will take 5 hours to close the 20 miles.
Answer choice E
Third, Plug In The Answers.
I usually like trying B and D, but the other choices look easier to work with.
Let's try C. B travels for 4 hours at 14 mph, so 56 miles. A would take 5.6 hours to do 56 miles, but A traveled for 2 hours alone and then 4 hours while B was also en route. That's not 5.6 hours.
Let's try E. B travels for 5 hours at 14mph, so 70 miles. A would take 7 hours to do 70 miles, which is exactly how long A traveled.
Answer choice E