## greatuser 2 years ago it took 2hrs

1. greatuser

it took 2hrs for boat to go from a to b with current and 6hrs to go back against curent. assuming constant speed of boat in both directions, how long wil it take raft (with speed equal to speed of curent) to go from a to b?

2. hartnn

let the boat (without any current) take 'x' hrs to reach from a to b and the raft (with speed equal to speed of current) take 'y' hrs to reach from a to b when current assist boat, total time taken was 2 hours, so x-y= 2 when current was against the boat, time taken was 6hrs , so x+y =6 find 'y' from here :)

3. greatuser

that means x=y+2=6-y which means y=2? that cant be right though

4. hartnn

yeah, i think i have overlooked something speed = distance / time here, distance is same so, speed * time will be constant let their speed be 'a' and 'b' so, (a+b)*2=(a-b)*6=distance =d and you need, time taken by raft, = d/b try it!

5. greatuser

but d and b are both unknown. how can we solve it?

6. greatuser

7. greatuser

so far, a= speed of boat b = sped of current 6a-6b = 2a + 2b meaning a = 2b

8. dumbcow

"d" is an arbitrary distance that is constant for all trips....let d=1 then 1/(a+b) = 2 1/(a-b) = 6 a = 2b 1/3b = 2 1/b = 6 --> b = 1/6 --> d/b = 6 it would take raft 6 hours

9. greatuser

oh i get i now thanks a lot