Math  /  Algebra

QuestionThe U.S. Dept of Transportation can complete a study on driving habits in 6 months. The U.S. Dept of Commerce can complete the same study in 10 months. How many months will it take to complete the study of driving habits if the two departments are working together?
HINT: Let us ignore reality and instead pretend that two bloated government bureaucracies will behave cooperatively and responsibly with your tax dollars.
Total Time == \square Answers may be written as unsimplified fractions or as decimals. If you choose decimals, round your answer to the nearest tenth decimal place.

Studdy Solution
Calculate the total time to complete the study.
The combined rate of work is 830 \frac{8}{30} of the study per month. To find the total time T T in months, take the reciprocal of the combined rate:
T=308 T = \frac{30}{8}
Simplify the fraction:
T=154 T = \frac{15}{4}
Convert to a decimal:
T=3.75 T = 3.75
Round to the nearest tenth:
T=3.8 T = 3.8
The total time to complete the study is 3.8 \boxed{3.8} months.

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