# Solving Word Problems With Quadratic Equations Then, the speed of the boat up the stream (or against the stream) = (x - $$\frac$$) km/hour, and the speed of the boat down the stream (or along the stream) = (x $$\frac$$) km/hour.Therefore, time taken to travel 10 km up the stream = $$\frac$$ hours and time taken to travel 5 km down the stream = $$\frac$$ hours.

Then, the speed of the boat up the stream (or against the stream) = (x - $$\frac$$) km/hour, and the speed of the boat down the stream (or along the stream) = (x $$\frac$$) km/hour.Therefore, time taken to travel 10 km up the stream = $$\frac$$ hours and time taken to travel 5 km down the stream = $$\frac$$ hours.

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The two galleries are separated by the distance of 70 m.

Where should a person stand for hearing the same intensity of the singers voice?

sorts of word problems, it is usually helpful to draw a picture.

Since I'll be cutting equal-sized squares out of all of the corners, and since the box will have a square bottom, I know I'll be starting with a square piece of cardboard.We know the roots of the quadratic equation ax$$^$$ bx c = 0, where a ≠ 0 can be obtained by using the quadratic formula x = $$\frac$$.1. Solution: Let the speed of the boat in still water be x km/hour. A boat can cover 10 km up the stream and 5 km down the stream in 6 hours.A square flower bed is prepared in its centre leaving a gravel path all round the flower bed.The total cost of laying the flower bed and gravelling the path at ₹3 and ₹4 per square metre respectively is ₹364. Solution(9) Two women together took 100 eggs to a market, one had more than the other. Step IV: Solve this equation to obtain the value of the unknown in the set to which it belongs.x = -5 does not satisfy the conditions of the problem length or breadth can never be negative. In solving a problem, each root of the quadratic equation is to be verified whether it satisfies the conditions of the given problem. Note that the second value could have been gotten by changing the sign on the extraneous solution.Therefore, from the question,$$\frac$$ $$\frac$$ = 6⟹ $$\frac$$ $$\frac$$ = 6⟹ $$\frac$$ $$\frac$$ = 3⟹ $$\frac$$ = 3⟹ $$\frac$$ = 3⟹ $$\frac$$ = 1⟹ 10x 5 = 4x$$^$$ – 9⟹ 4x$$^$$ – 10x – 14 = 0⟹ 2x$$^$$ -5x – 7 = 0⟹ 2x$$^$$ - 7x 2x - 7= 0⟹ x(2x - 7) 1(2x - 7) = 0⟹ (2x - 7)(x 1) = 0⟹ 2x - 7 = 0 or x 1 = 0⟹ x = $$\frac$$ or x = -1But speed cannot be negative.So, x = $$\frac$$ = 3.5Therefore, the speed of the board in still water is 3.5 km/h.(Hint: The ratio of the sound intensity is equal to the square of the ratio of their corresponding distances).Solution There is a square field whose side is 10 m.

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