Problem Solving

A boat traveled upstream a distance of 90 miles at avg speed of (v-3) miles per hour and than traveled the same distance downstream at an avg speed of (v+3)miles per hr.If the trip upstream took half an hour longer than the trip downstream . How many hours did it take the boat to travel downstream??

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A boat traveled upstream a distance of 90 miles at an average speed of (V-3) miles per hour and then travelled the same distance downstream at an average speed of (V+3) miles per hour.If the trip upstream half an hour longer than downstream, how many hours did it take the boat to travel downstream?

(*) 2.5
(*) 2.4
(*) 2.3
(*) 2.2
(*) 2.1

We can plug in the answers, which represent the number of hours that the boat took to travel downstream.
Since the trip upstream took 1/2 hour longer, the OA almost certainly is A -- the only answer choice that divides evenly into 90.

Answer choice A: 2.5 hours to travel downstream.
Rate downstream = d/t = 90/(2.5) = 36 hours.
Thus, v+3 = 36, implying that v=33.
Rate upstream = v-3 = 33-3 = 30 miles per hour.
Time upstream = d/r = 90/30 = 3 hours.
Time upstream - time downstream = 3-2.5 = .5.
Success!

The correct answer is A.

Please note the following:

-- Because we assessed the viability of the answer choices BEFORE we started to plug in, we had to try only ONE answer choice.

-- Plugging in the answers enabled us to determine the correct answer -- quickly and efficiently -- without having to set up and solve a quadratic equation.