Respuesta :
Step-by-step explanation:
the speed of the first ship is 20 mph
and the second ship is 15 mph
The speed of the ship that travelled North is 20 miles per hour and that of the ship that travelled East is 15 miles per hour.
Constant Speed:
'When the speed of an object remains the same - it does not increase or decrease - we say it is moving at a constant speed.'
According to the given problem,
Let the pirate ship that travelled north be A and the other ship that travelled east be B.
Since ship A went North which is upwards and ship B went east which is towards the right,
We can construct a right angled triangle with the perpendicular being the distance travelled by ship A and the base being the distance travelled by ship B.
It is given that after travelling for one hour, the ships are 25 miles apart.
Therefore we can consider the hypotenuse of the triangle to be 25 miles.
Now applying pythagoras theorem,
Hypotenuse² = Perpendicular² + Base²
⇒ 25² = x² + ( x + 5 )²
⇒ 625 = x² + x² + 10x + 25
⇒ 2x² + 10x + 25 - 625 = 0
⇒ 2x² + 10x - 600 = 0
⇒ x² + 5x - 300 = 0
⇒ x² + 20x - 15x - 300 = 0
⇒ x( x + 20 ) - 15( x + 20) = 0
⇒ ( x + 20 )( x - 15 ) = 0
⇒ x = 15 , -20
Since, distance cannot be negative,
x = 15
Therefore Distance travelled by ship A = ( 15 + 5 ) miles
= 20 miles
Time taken = 1 hour
Speed of ship A = [tex]\frac{Distance}{Time}[/tex]
= [tex]\frac{20}{1}[/tex] miles per hour
Distance travelled by ship B = 15 miles
Speed of ship B = [tex]\frac{15}{1}[/tex] miles per hour
Hence, after solving the problem, we can conclude that the speed of the ship travelling north is 20 miles per hour and the ship travelling east is 15 miles per hour.
Learn more about Constant Speed here:
https://brainly.com/question/18098874
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