Grade 7 Math POTW #16 Question:
Grade 8 Math POTW #16 Question:
Math POTW Optional Winter Break Grade 8 Solution #1:
Grade 8 Math POTW #15 Solution:
Grade 7 Math POTW #15 Solution:
Grade 7/8 Math POTW Optional Winter Break Solution #2:
Grade 8 POTW:
ReplyDeleteHappy 2019 people of the POTW world. When I first see this, I automatically think of the formula: d= st where d= distance, s=speed and t=time.
Since we know the hourly rate of each person, we can use that to find the formula for the total distance in terms of the time. The biker meets up with the walker 4 minutes after meeting up with the jogger. 4 minutes is equal to 1/15, so we can make the formula:
total time = time before the meet up +1/15
In the time before the meet up, the biker travelled 14t km and the walker travelled10t km.
Between the both of them, they travelled:
14t+10t= 24t km
Now we can make the other side of the equation (the other side of the equal sign):
In (t+ 1/15) hrs, the biker would have biked 14(t+1/15) and the waker would have walks 6(t+15)
Using this, we can form the following equation:
d= 14(t+1/15)+6(t+15) = 20(t+1/15)
Combine the two equations:
24t = 20(t+1/15)
24t=20t +4/3
4t=4/3
t=1.3 hrs
d=24t
d=24(1/3)
d=8
They are 8 km apart.
Grade 7 POTW
ReplyDeleteIn order to fid the depth of the water, I will have to find the area of each face of the aquarium. The front face is 450 cm squared and ABCD is 300 cm squared. The depth fully covers ABCD and covers 4/5 of the front base. 4/5 of 450 is exactly 360 cm and the height of the water when the base is ABCD is 24 cm. Therefore, the total volume of the water is 720 cm squared because the total volume of the tank is 900 cm squared and 4/5 of 900 is 720. When the aquarium is level, the depth is 12 cm with the base the one in the image.
Sorry this was wrong. The total volume of the tank is 9000 cm squared meaning the total volume of the water is 7200 cm squared because 4/5 of 9000 is 7200. When the aquarium is level, the depth is still 12 cm deep with the base the one in the image. When the aquarium was titled along AB, the depth of the water would be 24 cm.
Delete(24*15*20)/2
ReplyDelete3600 is area
Divide area by length and width
to get 6
Hellos.
ReplyDeleteGrade 8 POTW:
So I originally planned to do guess and check multiple times, because I was too lazy to figure out a better strategy (I was hungry).
So I originally guessed that the towns were 60 km apart (yes very far i know).
To calculate when the biker and the jogger met, then I added both their speeds and calculated who has what percentage of the total speed. (Biker is 14/24, 58.3%, Jogger is 10.24, 31.7%) Then, I calculated what those percentages are equal to in the actual distance. (58.3*60=35, 31.7*60=25) That meant the biker and the jogger would meet at a point 25 km away from Pi and 35 km away from Epsilonville. Now I did the same calculations but with the biker and the walker.
Biker: 14/20, 70%
Walker: 6/20, 30%
0.7*60=42
0.3*60=18
So the biker and the walker would meet at a point 18 kilometers from Pi, 42 kilometers from Epsilonville. That meant the biker traveled (25-18, or 42-35) 7 km in between to meet the jogger and then walker respectively, and since he/she bikes at 14 km/h, that would mean the difference in between in 30 minutes. At this point I realized my big mistake in guessing 60 km, which is way off the mark. However, since I know how long it actually takes the biker (4 minutes), I can just reset the whole calculations to scale. Since 30/4 is 7.5, I now just divide every distance number by 7.5. Since I originally guessed 60 km, I divide it by 7.5, which gives me the actual distance between the two towns. The distance between Epsilonville and Pi is 8 km.
Moral of the story: Don't try to walk 60 km.
Grade 8 POTW
ReplyDeleteFirst let's list what we know:
- walker travels 6km/h
- jogger travels 10km/h
- biker travels 14km/h
- biker travels from opposite direction and passes the jogger 4 minutes before passing the walker
To find out how far apart the towns pi and epsilonville are, we can use use algebra. Okay, so we know the biker meets the walker 4 minutes after passing the jogger. We can either convert 4 minutes into hours, or km/h to km/m. Km/m would be a large number, so we can convert the minutes. 4/60 = 1/15. Now we can start the actual calculations. The distance between the two points can be considered as 14t + 6t = 20t = d where t = time and d = distance. To get another value for the distance between the two points, we can use the fact that the biker meets the jogger 4 minutes before. In other words, 14(t - 1/15) + 10(t - 1/15) = 24(t - 1/15). We can now calculate for t.
20t = 24(t - 1/15)
20t = 24t - 8/5
8/5 = 4t
8/5/4 = 4t/4
2/5 = t
d = 20(2/5)
d = 8
Therefore, the distance between Pi and Epsilonville is 8km.
Grade 7 POTW
ReplyDeleteOkay, so when the water is tilted enough to cover ABCD, ⅘ of the base is covered. First, let’s find out what that is. 30(⅘) = 24. We need to find out how much water there is to know the depth of when it’s level. We can find the amount by calculating the volume of the water when it is tilted (still same volume). When the water covers ABCD, a right triangular prism is formed. The base would be 24 cm (we just found out), the height would be 15 cm (fully covers AD or BC), and the length would be 20 cm. The formula for volume of a triangular prism is (b x h x l)/2 = (24 x 15 x 20)/2 = 3600 cm^3. There is 3600 cm^3 (or mL) of water. To find out the depth of the water, we can divide the volume by the entire base (the bottom/top face). 3600/(30 x 20) = 6 cm.
Therefore, the depth of the water is 6 cm.
The area of side ABCD is 20*15=300, and ⅘ of 30 is 24.
ReplyDeleteThe volume of water is 300*24 = 7200.
To find the depth of the water, we have to divide this number by the area of the base.
7200/600= 12.
Now, since the water was in the shape of a triangular prism, we would divide this number by 2, giving us 6.
The depth of the water is 6 cm.
Good job Ananya!
DeletePOTW:
ReplyDeleteFirst, we need to determine the area of the side ABCD:
20 x 15 = 300, 4/5 of 30 is 24.
The volume of the water is 300 x 24, which equals 7200.
Now, to find the depth of the water, we divide this amount by the area of the base:
7200 / 600 = 12
We have one last step: the water was in the shape of a triangular prism, therefore we divide 12 by 2.
12 / 2 = 6cm.
So, the depth of the water is 6cm.
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ReplyDelete