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My sister and I found this answer by finding out how much distance each boat could travel in 15 minutes, since they only had sight of each other for 15 minutes.
We know that boat A can travel 8km/h, and 15 is 1/4 of an hour, so you would have to divide 8 by 4, which is 2. So, boat A travels 2km/15mins. (Since boat A only traveled 2 km in the 15 minutes, we knew that boat B would have to be faster)
Now, we know that they are in a 5000 m area and they are 200 m apart (from this point on, we decided to simplify it by converting km to m). Meaning that the remaining area is 4800 m. We know that boat A only traveled 2000 m in 15 minutes, so 4800 - 2000 = 2800.
So, boat B would have to travel 2800 m in order for them to lose sight of each other in 15 minutes.
Once again, 15 minutes is 1/4 of an hour, so 2800 x 4 = 11200m
11200m converted into km is 11.2 km, therefore boat B travels 11.2km/h
This is probably a bit trivial; can you both explain why did you decide to convert km into m? (you said that you meant to 'simplify'; why not the other way around if the average speed is measured by km/h?)
My Brother and I did this together to get that extra treat :D
2nd Way:
Opt 1 <----- Boat A -------200m--------Boat B ----->
Opt 2
Boat A ------> | | | 200m | | | <--------Boat B
Opt 3
A --- > | (200 m) | < --- B
Option 1 - Answer Above
Option 2 - They start 200 m apart (distance from side). Boat A traveled 8 km/h. 8 x 0.25 = 2 km. Therefore it traveled 2km in 15 minutes.
Boat B traveled 3 km in 15 minutes. 3 / 0.25 = 12. Therefore, it has a speed of 12 km/h.
Option 3 - The boats are 200 meters apart but will pass each other going the opposite direction. Boat A: 2 km - 0.2 m = 1.8 km 8km/h (speed) 2km in total, but passed 1.8km from Boat B
Boat B: 3 km + 0.2 = 3.2km 3.2 / 0.25 = 12.8km/h (speed) 3.2km in total, passed starting point
solved..what's the prize? =)
ReplyDeleteBoat B is faster, btw. Just look at it! it's made for speed. =)
Hello.
ReplyDeleteThe speed that boat B travels is 11.2km/h
My sister and I found this answer by finding out how much distance each boat could travel in 15 minutes, since they only had sight of each other for 15 minutes.
We know that boat A can travel 8km/h, and 15 is 1/4 of an hour, so you would have to divide 8 by 4, which is 2. So, boat A travels 2km/15mins. (Since boat A only traveled 2 km in the 15 minutes, we knew that boat B would have to be faster)
Now, we know that they are in a 5000 m area and they are 200 m apart (from this point on, we decided to simplify it by converting km to m). Meaning that the remaining area is 4800 m. We know that boat A only traveled 2000 m in 15 minutes, so 4800 - 2000 = 2800.
So, boat B would have to travel 2800 m in order for them to lose sight of each other in 15 minutes.
Once again, 15 minutes is 1/4 of an hour, so 2800 x 4 = 11200m
11200m converted into km is 11.2 km, therefore boat B travels 11.2km/h
- Jonathan and Rachel
Terrific explanation. =)
DeleteThis is probably a bit trivial; can you both explain why did you decide to convert km into m? (you said that you meant to 'simplify'; why not the other way around if the average speed is measured by km/h?)
We multiplied 2800 by 4 to find the distance traveled in an hour
ReplyDelete15 is 1/4 of 60 minutes
2800 x 4 = 11200
So, the speed would be 11.2 km/h
If we take this amount and divide it by 4, it would be 2.8 km or 2800 m.
My Brother and I did this together to get that extra treat :D
ReplyDelete2nd Way:
Opt 1
<----- Boat A -------200m--------Boat B ----->
Opt 2
Boat A ------>
|
|
|
200m
|
|
|
<--------Boat B
Opt 3
A --- >
|
(200 m)
|
< --- B
Option 1 - Answer Above
Option 2 - They start 200 m apart (distance from side). Boat A traveled 8 km/h. 8 x 0.25 = 2 km. Therefore it traveled 2km in 15 minutes.
Boat B traveled 3 km in 15 minutes. 3 / 0.25 = 12. Therefore, it has a speed of 12 km/h.
Option 3 - The boats are 200 meters apart but will pass each other going the opposite direction.
Boat A:
2 km - 0.2 m = 1.8 km
8km/h (speed)
2km in total, but passed 1.8km from Boat B
Boat B:
3 km + 0.2 = 3.2km
3.2 / 0.25 = 12.8km/h (speed)
3.2km in total, passed starting point
Excellent answers. Thorough, clear, and in a variety of ways! Please see me for a treat this week!
ReplyDelete(Yes, the correct answer was 11.2km/h.