# Solving Word Problems With Quadratic Equations

Had the speed been 15 km/hour more it would have taken 30 minutes less for the journey. Solution(6) From a group of 2x black bees , square root of half of the group went to a tree.

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We will discuss here how to solve the word problems using quadratic formula. If the speed of the stream is 1.5 km/h, find the speed of the boat in still water.

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.

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?(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.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. 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.The remaining two got caught up in a fragrant lotus. Solution(7) Music is been played in two opposite galleries with certain group of people.In the first gallery a group of 4 singers were singing and in the second gallery 9 singers were singing.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.