This question involves the Distance Formula and can be solved by TESTing VALUES.
Distance = (Rate)(Time)
We're told a few things about a kayaker:
1) She travels upstream at M km/hour
2) She travels downstream at N km/hour
3) Total TIME traveled is P hours
We're asked for the DISTANCE traveled UPSTREAM....
For this question, we're going to choose the two speeds AND the distance traveled....this will help us figure out the time traveled in each direction (and thus, the TOTAL TIME).
M = 2 km/hour upstream
N = 3 km/hour downstream
Distance = 6 km in each direction
D = (R)(T)
6km = (2km/hour)(T)
6/2 = T
T = 3 hours upstream
D = (R)(T)
6km = (3km/hour)(T)
6/3 = T
T = 2 hours downstream
P = TOTAL Time = 5 hours
We're asked for the DISTANCE traveled upstream, so we're looking for an answer that = 6 when M = 2, N = 3 and P = 5.
Answer A: (M)(N)(P) = (2)(3)(5) = 30 NOT a match
Answer B: MN/P = (2)(3)/(5) = 6/5 NOT a match
Answer C: (M+N)/P = (2+3)/5 = 5/5 NOT a match
Answer D: MNP/(M+N) = 30/5 = 6 This IS a MATCH
Answer E: PM/N - PN/M = 10/3 - 15/2 = Negative NOT a match
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