# The speed of a bo

Given: The speed of a boat in still water is 8 km / hr. It can go 15 km upstream and 22 km downstream in 5 hours.

To find: the speed of the stream.

Solution:

Let the speed of stream be ‘a’ km/hr.

Given, speed of a boat in still water is 8 km / hr. It can go 15 km upstream and 22 km downstream in 5 hours.

Going upstream means that boat is going in opposite direction of the stream so speeds will be added and going downstream means that the boat is going in the same direction of the stream.

So,

Relative speed of boat going upstream = 8 – a

Relative speed of boat going downstream = 8 + a

Time = distance/speed

Total time is given to be 5 hrs.  ⇒15(8+a) + 22(8-a) = 5(8-a)(8+a)

Apply the formula (a-b)(a+b)= a2-b2 in (8-a)(8+a)

Here a=8 and b=a.

⇒ 120 + 15a + 176 – 22a = 5(64 – a2)

⇒ 296 – 7a = -5a2 + 320

⇒ 5a2 – 7a – 24 = 0

Factorize the equation by splitting the middle term

⇒ 5a2 – 15a + 8a – 24 = 0

⇒ 5a(a – 3) + 8(a – 3) = 0

⇒ (5a + 8)(a – 3) = 0

⇒ (5a + 8) = 0 and (a – 3) = 0  ⇒ a = 3 km/hr

Hence speed of the stream is 3 km/hr.

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