Question

23. A motor boat whose speed is 35 km/hr
in still water takes 3 hour more to go
100 km upstream then to return
downstream to the same spot. The
speed of the stream is​

Answer 1

Answer:

15

Step-by-step explanation:

Let the speed of stream be x

Time upstream = 100/35-x

Time downstream = 100/35+x

100/35-x  - 100/35+x = 3    

100(35+x) - 100(35-x) = 3(35² - x²)

3500+100x - 3500 + 100x = 3675 - 3x²

3x² + 200x - 3675 = 0  

Discriminant =200²+210²= 40000+44100=84100

x = -b±√84100/ 2a

=  -200±290/ 2*3

= 90/6 or -490/6

= 15 or -490/6

Speed of stream = 15 (speed cannot be negative)

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr