SOLUTION: If a teacher can finish a test 3 times faster than a student that finishes it in 40 minutes how would you write an equation to determine how many minutes it would take for both tea

Question 864629: If a teacher can finish a test 3 times faster than a student that finishes it in 40 minutes how would you write an equation to determine how many minutes it would take for both teacher and student to finish the test if working together? Would equation be 1/x +1/3x=1?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39626) (Show Source): You can put this solution on YOUR website!
The quick agent does a job three times faster than a regular agent. The regular agent can do a job himself in 40 minutes. What would be the work rate for both agents working at the same time on the job?

Use rates as JOBS per MINUTES.
Quick agent, .... Look at the regular agent first.
Regular Agent, jobs per minute.
Quick Agent, jobs per minute; shown this way because "three times faster...".

Quick And Regular Agents together, SUM OF THEIR INDIVIDUAL RATES.
JOBS per MINUTE.

, ONE JOB IN TEN MINUTES.

You can take the reciprocal and say, "ten minutes needed for both agents together to do one job".
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The student's rate is:
( 1 test finished ) / ( 40 min )
The teacher's rate is:
( 1 test finished ) / ( 40/3 min )
---------------------------
Let = time in minutes to finish test
with both working on it together
Their rate working together:
( 1 test finished ) / ( t min )
-------------------------
Add their rates to get rate working together

Then you would multiply both sides by

min

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