Question

a Boat goes 15 km upstream and 10 1 /2 km downstream in 3 hours 15 minutes it goes 12 km upstream and 14 km downstream in 3 hours what is the speed of the boat in still water ?

Answer 1

Let downstream speed be x and upstream speed be y
so,
10.5/x + 15/y = 3 hr 15 mins = 3 + 0.25 hr = 3.25
10.5/x + 15/y = 3.25....(1)
And
14/x + 12/y = 3....(2)

Let 1/x = p and 1/y = q
So,we have
10.5p + 15q = 3.25....(3)
14p + 12q = 3....(4)
Solving (3) and (4), we get
14p + 12q = 3
q = (3 - 14p)/12

Putting in (3), we get
10.5p + 15(3 - 14p)/12 = 3.25
10.5p + 5(3 - 14p)/4 = 3.25
42p/4 + (15 - 70p)/4 = 3.25
42p + 15 - 70p = 13
28p = 2
p = 1/14
so, q = [ 3 - 14(1/14) ]/12
q = (3 - 1)/12 = 1/6
So, x = 14 and y = 6
Downstream = 14 = speed of boat + speed of water
Upstream = 6 = speed of boat - speed of water
let speed of boat be b and speed of water be w, so
b + w = 14b - w = 6
So, 2b = 20
b = 10
Therefore, speed of boat in still water = 10 km/hr