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The steamboat makes the trips in 5 hours. The yacht makes the boat in 2.5 hours. The yacht is 20 knots faster than the steamboat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?

Respuesta :

Cricetus

Answer:

Steam boat = 20 Knots , Yacht = 40 Knots

Step-by-step explanation:

Let the distance travelled by both the boats be x

Case 1: Steamboat

Speed [tex]S_{s}=\frac{x}{5}[/tex]

Case 2 : Yacht

[tex]S_{y}=\frac{x}{2.5}[/tex]

[tex]S_{y}=\frac{2x}{5}[/tex]

Also given that speed of yacht is 20 more than that of steamboat

[tex]S_{y} -S_{s}=20[/tex]

Hence

[tex]\frac{2x}{5} - \frac{x}{5} = 20[/tex]

[tex]\frac{x}{5} = 20[/tex]

[tex]x = 100[/tex]

Hence the distance traveled is 100 naut miles

Hence

Speed of Steam boat = [tex]\frac{100}{5}[/tex]  = 20 Knots

Speed of Yacht = [tex]\frac{100}{2.50}[/tex]  = 40 Knots

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