Mr. Jacobs can correct 150 quizzes in 50 minutes. His student aide can correct 150 quizzes in 75 minutes. Working together, how many minutes will it take them to correct 150 quizzes? (This is a test release question on the California High School Exit Exam)
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Find out how many quizzes each can grade in 1minute.
j=150/50 = 15/5 = 3 quizzes per minute
s=150/75 = 6/3 = 2 quizzes per minute.
together j+s can do ? per minute?
2+3 = 5 quizzes per minute.
150/5 = 30/1 = 30 minutes to correct them all?
thank you that was very helpful.
I have one more question. Can you please help me set up the problem? It is similar, I think.
Ricardo runs 10 minles each Saturday. If he doubles his usual speed, he can run the 10 miles in one hour less than his usual time. What is his usual speed?
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The unknowns are his usual speed; lets call that x. And his usual time; lets call that y.
(twice)x = y - 1(hour)
2x = y-1
His usual speed (x) = (y-1)/2.
If you knew his usual time; then you could find his usual speed.
Lets do it this way:
Speed = distance/time
x=10/y and x= 10/2(y-1)
To make x=x; we equate the 2 equations:
10/y = 10/2(y-1)
the 10s cancel each other out and we are left with:
2 = 2y-y
His normal speed is 10 miles in 2 hours: or 5 mph
When he doubles his speed to 10 mph; he takes 1 hour instead of 2 to do it which answers the question :)
usual speed = 5mph....