two dogsled teams raced across a 300 mile course in wyoming. team a finished the course in 3 fewer hours than team q. if team a ' s average speed was 5 mph greater than team q ' s, what was team q ' s average mph?	Choose the correct answer:  A) 12  B) 15  C) 18  D) 20  E) 25
<gadget id="calculator">300 / 5</gadget>
<output>60</output>

<gadget id="calculator">60 / 3</gadget>
<output>20</output>

<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 q. if team a ' s average speed was 5 mph greater than team q ' s, what was team q ' s average mph?
divide(divide(300, 5), 3)
"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 q ' s speed was s . then team q ' 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 q . 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 wo n ' 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 d , you find the time for team q is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."