Problem Solving

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

A) 2.5

B) 2.4

C) 2.3

D) 2.2

E) 2.1

[spoiler]A
[/spoiler]

solu:

(y-3) = 90/a+0.5 -----> 1 ( a is in hours, while upstream)
(y+3) = 90/a -------> 2 (while downstream)

By equating two equations we get a = (y-3)/12 - - - (distances are equal)

by substituting the same in 2 equation i get y as 33 and by substituting in above equation.

I got as 2.5

speed = distance/time

Upstream:

v-3 = 90/t+0.5

Downstream:

v+3 = 90/t

Now use backsolving strategy, and the easiest would be to choose 2.5

Upstream

v-3 = 90/3 or v-3 = 30, hence time = 3hrs

Downstream

v + 3 = 90/2.5 or v+3 = 36, hence time = 2.5 hrs

Difference between upstream and downstream = 30 mins

Choose A

Remember GMAT is not checking your calculation skills, so any answer choice that involves too much of calculation should be avoided.

in the above question I would have tried 2.5 and then 2.1. Reasoning: if the time taken downstream is 2.5 hrs then upstream it would be 3hrs and it does not involve too much calculation. If the time downstream is 2.1 then upstream it would be 2.6 hrs or 2 and 1/10th of an hour. the rest of the choices involve too much calculation