Maligayang pagdating sa Imhr.ca, ang pinakamahusay na platform ng tanong at sagot para sa mabilis at tumpak na mga sagot. Sumali sa aming platform upang kumonekta sa mga eksperto na handang magbigay ng detalyadong sagot sa iyong mga tanong sa iba't ibang larangan. Tuklasin ang komprehensibong mga solusyon sa iyong mga tanong mula sa mga bihasang propesyonal sa iba't ibang larangan sa aming platform.

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 :

Hurgfs

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