SOLUTION: You have 89 minutes to take an exam of 33 questions.After you finish the first 12 questions you realize you must answer the remaining questions twice as fast to finish the exam. H

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Question 949338: You have 89 minutes to take an exam of 33 questions.After you finish the first 12 questions you realize you must answer the remaining questions twice as fast to finish the exam. How many questions per minute were you answering?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let q/m equal the number of questions per minute for the first 12 questions.

let 2q/m equal the number of questions per minute for the last 21 questions.

you have 89 minutes to take the exam.

the number of questions divided by the number of questions per minute gives you the number of minutes.

this is because q / (q/m) is equal to q * m/q which is equal to m.

so you need to divide the number of questions by the number of questions per minute to get the minutes.

you know that the total minutes is equal to 89

you know that the rate for the first 12 questions is q/m.

you know that the rate for the last 21 questions is 2q/m.

your formula becomes:

12/(q/m) + 21/(2q/m) = 89

this is equivalent to 12m/q + 21m/(2q) = 89

multiply both sides of this equation by 2q to get:

2*12m + 21m = 89*2q)

simplify to get:

24m + 21m = 178q

combine like terms to get:

45m = 178q

divide both sides of this equation by m and divide both sides of this equation by 178 to get:

45/178 = q/m

you have:

q/m = 45/178

2q/m = 90/178

you were answering 45/178 questions per minute for the first 12 questions.

you were answering 90/178 questions per minute for the last 21 questions.

12 / (45/178) + 21 / (90/178) is equal to:

12 * 178/45 + 21 * 178/90 which is equal to 89 minutes.

solution looks good.

this can also be solved using the rate * time = quantity formula.

let x = the rate for the first 12 questions.

let t1 = the time for the first 12 questions.

you get x*t1 = 12.

solve for t1 to get t1 = 12/x

let 2x = the rate for the last 21 questions.

let t2 = the time for the last 2 questions.

you get 2x*t2 = 21

solve for t2 to get t2 = 21/2x.

you know that t1 + t2 = 89 minutes.

replace t1 with 12/x and replace t2 with 21/2x to get:

12/x + 21/(2x) = 89

multiply both sides of this equation by 2x to get:

24 + 21 = 89*2x which becomes 45 = 178x

divide both sides of this equation by 178 to get x = 45/178.

that makes 2x = 90/178.

x is the same as q/m which is the questions per minute for the first 12 questions.

2x is the same as 2q/m which is the questions per minute for the last 21 questions.

the solutions are the same.

you're good either way.