Problem Solving

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

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1

[spoiler]OA: A[/spoiler]

I think Answer is A 2.5

Here is the solution:

UP DOWN
Sp: v-3 v+3
Di: 90 90
Ti: t1 t2
now, t1 = t2 +0.5
and T = D/S
t1 = 90/(v-3)
t2 = 90/(v+3)
solving above give the value of v and than t.

Hi
Can some one explain this one pls.
thanks

Hi RI,

let t be the time take downstream

so t+.5 is the time taken upstream

hence t =90/(v+3) & t+0.5 = 90/(v-3)

here if we isolate v to the LHS of both the expressions, then we can construct a simple quadratic eqn, solving which we can get the only postive root as 2.5 which is required.

thanks Samir, I was making some simple mistakes while solving the equations, got the basic ones correct then made stupid mistakes later..

hi,
can someone post the equation solution on this post?
cannot solve the equation.

I dont understand what the lhs is? ALso I am not following in th emath for some reason. CAn we simplify this more or even backsolve it?

can someone pls post the eq solution.

can someone please post the step by step, I'm doing equations and everything and it still does not work out.

the answer is 2.5
steps:
distance d=90
upstream speed=v-3
downstream speed = v+3
speed = distance/timetaken

90/(x+0.5)=v-3------1

90/x= v+3--------2

from 1 we get

v = 3+ 90/(x+0.5)

substitute v in 2 we get the quadratic equation

6x^2+3x-45=0----------3

solving 3 we get the roots as 2.5 and -3.........since time cant be negative the answer is 2.5

correct me if i am wrong

The actual algebra on this question is WAY above normal GMAT levels - where is the question from?

This is from practice test 1 of GMAT prep

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

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1

[spoiler]OA: A[/spoiler]

Could someone pls. write all the steps of the equation ?
Even plugging in the correct answer (2,5) in T I can't reach a reasonable equation.

(v-3) * (3) = (v+3) * 2,5

V=33 then 36T=45T !!!!

May be some Math Guru who can think this problem without making so many calculations? Tksvm!!

SPEED = DIST/TIME

If Upstream trip = 2.5 hours, than downstream = 2.0 hours

For upstream
speed = distance/time
(v-3)=(90/2.5)
(v-3)=36
v=39

For downstream
speed = distance/time
(v+3)=(90/2)
(v+3)=45
V=39... and bob's your uncle!
This solution works, so stop here

but just to prove this works, let try solution B

If upstream was 2.4 hours, than downstream = 3.9 hours

For upstream
speed = distance/time
(v-3)=(90/2.4)
(v-3)=37.5
v=40.5

For downstream
speed = distance/time
(v+3)=(90/3.9)
(v+3)=23ish
V=20ish
does not work!

Just another explanation.. I am hoping that it is simpler to understand..

We need to just equate the times taken for upstream and downstream considering that downstream it takes 0.5 hours lesser and use the speed, distance and time formula.

Time = Distance/speed

Upstream time taken = 90/(v-3) --- (1)

Downstream time taken = 90/(v+3) --- (2)

According to question, downstream is 0.5 hours lesser than upstream, this implies

90/(v-3) = 90/(v+3) + 0.5 -- (1)

6/(v^2 - 9) = 1/180

V^2 = 1089

v = 33 -- (3)

So apply (3) in (2), we get

90/(33+3) = 2.5 Hours and that's the answer..