Question

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Answer 1

Let the speed of the the boat is xkm/hr.

Let the speed of the stream be ykm/hr.

(i)

Given that boat goes 30 km upstream and 44 kms downstream in 10 hours.

Speed upstream + Speed downstream = Time taken

⇒ (30/x - y) + (44/x + y) = 10

Let x - y = u and x + y = v.

⇒ 30u + 44v = 10

(ii)

Given that it can go 40km upstream and 55km downstream in 13 hours.

⇒ (40/x - y) + (55/x + y) = 13

Let x - y = 40 = u and x + y = v.

⇒ 40u + 55v = 13.

Elimination Method:

On solving (i) *4 & (ii) * 3, we get

⇒ 120u + 176v = 40

⇒ 120u + 165v = 39

   ------------------------

                11v = 1

                  v = 1/11

Then, x + y = 11.   ----- (iii)

Substitute v = (1/11) in above equations, we get

⇒ 120u + 176v = 40

⇒ 120u + 176(1/11) = 40

⇒ 120u + 16 = 40

⇒ 120u = 24

⇒ u = (1/5).

Then, x - y = 5.    ----- (iv)

Now,

On solving (iii) & (iv), we get

⇒  x + y = 11

⇒ x - y = 5

   ----------------

    2x = 16

       x = 8

Substitute x = 8 in (iv), we get

⇒ x - y = 5

⇒ 8 - y = 5

⇒ y  = 3.

Therefore:

⇒ Speed of the boat = 8 km/hr.

⇒ Speed of stream = 3 km/hr.

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