Makahanap ng eksaktong solusyon sa iyong mga problema sa IDNStudy.com. Hanapin ang impormasyon na kailangan mo nang mabilis at madali sa pamamagitan ng aming komprehensibo at eksaktong platform ng tanong at sagot.

an 8-hour river cruise goes 12km upstream and then back. The speed of the river current is 2kph. What is the speed of the boat in still water?​

Sagot :

Answer:

4kph

Step-by-step explanation:

Let x be the speed of the boat

Speed of the river  = 2 kph

Total time spent = 8 hours

Distance = 12 km

Speed of the boat upstream ( against the river current) = x - 2

Speed of the boat downstream ( along with the current ) = x +2

The formula for t =  d/s

Where

d is distance

s is speed

Therefore the working equation would be

time for downstream + time for upstream = 8 hours

[tex]\frac{12}{x+2} + \frac{12}{x-2} = 8[/tex]

Multiplying both sides (x+2)(x-2) by  for the purpose of eliminating fractions

[tex]\frac{12(x+2)(x-2)}{x+2} + \frac{12(x+2)(x-2)}{x-2} = 8(x+2)(x-2)\\[/tex]

Cancel same terms

12(x-2) + 12(x+2) = 8(x+2)(x-2)

Solving further

[tex]12x-24+12x+24 = 8x^2 - 32[/tex]

[tex]24 x = 8x^2 - 32\\8x^2 -24x- 32 = 0\\x^2 - 3x -4 = 0\\\\\text {Factoring}\\(x-4)(x+1) = 0[/tex]

Finding the roots

x-4 = 0

x = 4

x+1 = 0

x = -1

Disregarding the negative value of x ,

The answer therefore is 4 kph for the speed of the boat in still water

Checking

[tex]\frac{12}{4+2} + \frac{12}{4-2} = 8\\2+6 =8\\8 =8[/tex]

#CarryOnLearning