anonymous one year ago Working at a constant rate, Bob can produce x/3 widgets in 8 minutes. Working at a constant rate, Jack can produce 2x widgets in 40 minutes, where x>0. Which of the following is greater? A. The number of minutes it will take Bob to produce 5x widgets. B. The number of minutes it will take Jack to produce 6x widgets.

1. dakid88

B.

2. anonymous

i dont want the answer i want to know how to do it go away

3. anonymous
4. dakid88

stop cursing

5. FireKat97

@yomamabf so firstly, you want to start off by writing the equations so that you can see how many widgets each person makes in a minute

6. phi

I would first write down a "rate" Bob. How many widgets per minute can he make? Write the ratio of widgets divided by time, and simplify. can you do that ?

7. anonymous

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8. anonymous

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9. phi

yes. we have this question The number of minutes it will take Bob to produce 5x widgets. now we use rate * time = amount we have the rate = x/24 we have the amount 5x solve for time

10. anonymous

I don't understand why i have to multiply 5 by 24 tho. The 5x is throwing me off

11. phi

First, we are only doing Bob's problem. Bob makes x/24 widgets per minute (that is his rate) we want 5x widgets we use rate*time = amount and fill in the rate and the amount to get this equation $\frac{x}{24}\cdot t = 5x$ (I used "t" for time) ok so far ?

12. anonymous

yep

13. phi

now "solve for t" using normal algebra can you do that ? (I would multiply both sides by 24/x)

14. anonymous

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15. anonymous

is that right?

16. phi

yes, and that means t= 120 minutes

17. anonymous

got it thanks phi!!

18. phi

It takes Bob 120 minutes to make 5x widgets (notice we don't know what 5x means as a number, but we don't care)

19. phi

now we do the same thing for Jack. what is Jack's rate ?

20. anonymous

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21. anonymous

the same 120

22. anonymous

right?

23. phi

Jack's rate is 2x/40 (the ratio of number of widgets divided by time) you can simplify that to x/20 now do rate * time = amount where rate= x/20 and amount is 6x

24. anonymous

Hey another question can i just substitute the x for a 1 since x>0?

25. phi

it would be dangerous to put in a number for x notice when you solve this problem the x "goes away" and we get a simple number for the answer. But if the x did not divide out, it would be part of the answer. In this problem we could let x= 1 and we would get the correct answer. But we only know that because we solved the problem first using "x" and noticed it cancelled out.

26. anonymous

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27. anonymous

ohhhhh i see so it's not a good idea. okay gotcha!