In this page quadratic equation practical solution6 we are going to see solution of practice question of the worksheet quadratic equation practical application.

Question 6:

The speed of a boat in still water is 15 km/hr. It goes 3 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.

Solution:

Let “x km/hr” be the speed of water

Speed of boat is 15 km/hr

So speed is upstream = (15 + x) km/hr

Speed in downstream = (15 –x) km/hr

Let T1 be the time taken to cover the distance 30 km in upstream

Let T2 be the time taken to cover the distance 30 km in downstream

Time = Distance/Speed

T1 = 30/(15 + x)

T2 = 30/(15 - x)

T1 + T2  = 4 hours 30 minutes

T1 + T2  = 4 ½

[30/(15 + x) + 30/(15 - x)] = 9/2

30[1/(15 + x) + 1/(15 - x)] = 9/2

30 [(15 – x + 15 + x)/(225 - x²)] = 9/2

30 (30)/(225 - x²) = 9/2

900 x 2 = 9 (225 - x²)

Now let us divide the entire equation by 9

So that we will get 200 = (225 - x²)

225 - x²  = 200

225 – 200 = x²

x² = 25

x = √25

x = ± 5

Speed must be positive so x = 5 is the required speed.

Speed of water = 5 km/hr

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