The Lake House: Mike and Tina's Race to the Sauna

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In summary, the lake house is located in A and the beach house B is located on an island, with a distance of 675 m between them. Mike walks at a speed of 6.9 km/h towards the sauna at point C, arriving there in 10 minutes. Tina also leaves the island by boat and arrives at the sauna 4 minutes earlier than Mike. Using the Pythagorean theorem, the distance between B and C is found to be 1.353 km. Therefore, the average speed of Tina's boat is 13.53 km/h.
  • #1
chawki
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Homework Statement


The lake house is located in A, which is home of Mike. Against the shore, perpendicular to the 675 m distance is the island's beach house B, which is home of Tina. Mike walks along the beach at a speed of 6.9 km/h toward the sauna and the C arrives there exactly 10 minutes. At the same time Tina also leaves the island by boat lakeside sauna and the C arrives there exactly 4 minutes earlier than Mike.

Homework Equations


What was the average speed of the boat?


The Attempt at a Solution


x2=0.6752+1.1042
x=1.294Km (distance from B to C)

Tina arrives 4minutes earlier than Mika means she arrives in 10-4=6min=0.1h
Average speed = 1.294/0.1=12.94km/h=3.594m/s
 

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  • #2
Is 1.104 supposed to be the distance from A to C? It doesn't look like 6.9 * 1/6.
 
  • #3
yes it is.
distance from A to C = 6.9*0.16=1.104Km
 
  • #4
chawki said:
yes it is.
distance from A to C = 6.9*0.16=1.104Km

Interesting about rounding. 10 min/ 60 min is 0.16666etc., which rounds to 0.17 (have to round up), producing a distance of 1.173 km.

Simply dividing by 6 (*10/60) gives 1.15 km exactly.

You seem to be doing the rest the right way.
 
  • #5
I don't know where you got 1.15km or what it is!

by using the phytagorean law, i found the distance from B to C is 1.353km.
Then the speed would be 1.353/0.1 = 13.53km/h

but I'm still wondering why they said average speed..obviously it's just a speed.
 
  • #6
chawki said:
I don't know where you got 1.15km or what it is!

by using the phytagorean law, i found the distance from B to C is 1.353km.
Then the speed would be 1.353/0.1 = 13.53km/h

but I'm still wondering why they said average speed..obviously it's just a speed.

1.15km is the distance A to C. You are using 1.104 based on improper rounding. I didn't bother to calculate how much this affects your result.
 
  • #7
no i used 1.173km
 

FAQ: The Lake House: Mike and Tina's Race to the Sauna

What is "The Lake House: Mike and Tina's Race to the Sauna" about?

"The Lake House: Mike and Tina's Race to the Sauna" is a fictional story about two friends, Mike and Tina, who are determined to be the first ones to reach the sauna at their family's lake house. The story follows their journey as they encounter obstacles and use their scientific knowledge to overcome them.

Who wrote "The Lake House: Mike and Tina's Race to the Sauna"?

"The Lake House: Mike and Tina's Race to the Sauna" was written by a team of scientists and writers, who wanted to create a fun and educational story that incorporates scientific concepts and principles.

What scientific concepts are included in "The Lake House: Mike and Tina's Race to the Sauna"?

The story incorporates various scientific concepts such as physics, chemistry, biology, and environmental science. Some examples include energy and motion, buoyancy, heat transfer, and natural ecosystems. These concepts are presented in a way that is easy for children to understand and apply to real-life situations.

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Yes, "The Lake House: Mike and Tina's Race to the Sauna" is suitable for all ages. While the story is primarily targeted towards children, adults can also enjoy the scientific themes and lessons presented in the story.

Can "The Lake House: Mike and Tina's Race to the Sauna" be used as an educational tool?

Yes, "The Lake House: Mike and Tina's Race to the Sauna" can be used as an educational tool in classrooms or at home. The story provides a fun and engaging way for children to learn about various scientific concepts and their applications in everyday life.

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