Boats in Water

Speed of boat in still water = x

Speed of stream(current) of water = y

then 

Upstream speed (U_s): x - y (Against current of stream)

Downstream speed (D_s) : x + y (In direction of stream)

Speed of boat in still water (x) = (U_s + D_s)/ 2

Speed of stream (current) (x) = (D_s - U_s)/ 2 

Q1. If speed of boat in still water is 10 m/s & speed of current of water is 3 m/s. Find the time taken by boat to cover distance of 70 m moving against current of water. 

(1) 7s  (2) 10s (3) 23.33s (4) 5.33s (5) None of these.

Solution:-

Since boat is going against stream of water,it relative speed would be upstream speed = 10 - 3 = 7 m/s.

Time required = 70 / 7 = 10 s

Q2.Speed of boat in downstream is twice speed when it is upstream. What is ratio of speed of current to speed of boat in still water ?
(1) 3:1  (2) 1:3 (3) 2:1 (4) 1:2 (5) 3:2

Solution:-
let the speed of boat in still water be x m/s.
& speed of current be y m/s.
Downstream Speed= 2 Upstream Speed
x +y = 2(x-y)
x + y = 2x - 2y
x = 3y
so y:x  = 1:3 

Q3. what is ratio of time taken by a boat to move from A to B against the current of speed & on its return journey to A ?

1. Upstream speed : Downstream speed
2. Downstream speed : Upstream speed 
3. Average of Downstream speed & Upstream speed  
4. One-way distance  : avg speed
5.Two-way distance  : avg speed

Solution:-
while going it is upstream speed & on return journey it is downstream speed.
We know that time & speed are inversely proportional hence ratio would be Downstream speed : Upstream speed . Hence answer option 2.
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