Question

speed of a boat in still water is 11 km per hour. it can go 12km upstream and return to the original point in 2hrs45 min. find the speed of boat

Answer 1

Given
speed of boat in still water = 11 km/hr

Let the speed of stream be x km/hr

Speed of boat upstream = (11 – x) km/hr

Speed of boat downstream = (11 + x) km/hr

Given distance travelled upstream = 12 km

Total time taken = 2 hr 45 min = (11/4) hrs

Time taken for upstream journey = 12/(11 – x)

Time taken for downstream journey = 12/(11 + x)

ATQ

[12/(11 – x)] + [12/(11 + x)] = (11/4)

12 ( 1/ 11 -x + 1/ 11 + x ) = 11 / 4

22 / 121 - x^2 = 11 / 4*12

22/ 121  - x^2  = 11 / 48

1331 - 11 x^2  = 1056 

11 x^2 = 275 

 x^2 = 25 

x = +5 or -5

As speed can't be negative, x not equal to -5.

we get x = 5


Thus speed of stream is 5 km/hr

Answer 2

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Let the breadth of mango grove be l.

Length of mango grove will be 2l.

Area of mango grove = (2l) (l)= 2l2

2l2 = 800

l2 = 800/2 = 400

l2 – 400 =0

Comparing the given equation with ax2 + bx + c = 0, we get

a = 1, b = 0, c = 400

As we know, Discriminant = b2 – 4ac

=> (0)2 – 4 × (1) × ( – 400) = 1600

Here, b2 – 4ac > 0

Thus, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.

l = ±20

As we know, the value of length cannot be negative.

Therefore, breadth of mango grove = 20 m

Length of mango grove = 2 × 20 = 40 m