IS this correct? If not why not? Is there another proportion that Ken could set
ID: 3007129 • Letter: I
Question
IS this correct? If not why not? Is there another proportion that Ken could set up to solve the problem? (The area of a circle that has radius r units is pir^1 square units.) In a cookie factory. 4 assembly lines make enough boxes of cookies to fill a truck in 10 hours. How long will n take to fill the truck if 8 assembly lines arc used? Is the proportion appropriate for this situation? Why or why not? If not. can you solve the problem another way? (Assume that all assembly lines work at the same steady rate) In the cookie factory of part 2. how long will it take to fill a truck if 6 assembly lines are used? (If you gel stuck here, move on to the next problem and come back.) Robyn used the following reasoning to solve the previous problem: Since 4 assembly lines fill a truck in 10 hours. R assembly lines should fill a truck in half that time, namely, in 5 hours Since 6 assembly lines is halfway between 4 and 8. it ought to take halfway between 10 hours and 5 hours, or 71/2 hours, to fill a truck. Robyn's reasoning seems quite reasonable, but is it really correct? Let's look carefully.Explanation / Answer
2.
4 assembly lines take 10 hours
Hence Each assembly line fills quarter of truck in 10 hours
So each assembly line fills whole truck in :4*10 hours
So the ratio is wrong. We need to multiply number of assembly lines with number of hours not divide
Hence, 4*10=8*x
Giving, x=5 hours
So 8 assembly lines fill the truck in 5 hours
3.
Let x be the number of hours
Hence, x*6=4*10
giving, x=40/6=20/3 hours
4.
Let, k be number of assembly lines and x be number of hours
Hence, kx=4*10 or x=40/k
# of assembly lines # of hours to fill truck
1 40
2 20
4 10
8 5
16 2.5
32 1.25
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