Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team W. If team A's average speed was 5 mph greater than team W's, what was team W's average mph?
Choose the correct choice from the following
A) 12 B) 15 C) 18 D) 20 E) 25
This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.   Say Team W's speed was s. Then Team W's time is 300/s.   Team A's speed was then s+5, and Team A's time was then 300/(s+5).   We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team W. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer 20, you find the time for Team W is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, 20 is correct.
<result>D</result>
Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team W. If team A's average speed was 5 mph greater than team W's, what was team W's average mph?