Alicia can row 6 miles downstream in the same time it takes her to row 4 miles upstream. She rows downstream 3 miles/hour faster than she rows upstream. Find Alicia’s rowing rate each way. Round your answers to the nearest tenth, if necessary.''
A.4 mi/h downstream, 2.7 mi/h upstream
B.20 mi/h downstream, 13.3 mi/h upstream
C.2.7 mi/h downstream, 4 mi/h upstream
D.9 mi/h downstream, 6 mi/h upstream
To solve this problem, let's denote Alicia's rowing rate upstream as x miles/hour. This means her rowing rate downstream would be x + 3 miles/hour.
The time it takes for Alicia to row 6 miles downstream is given by 6/(x+3), and the time it takes for her to row 4 miles upstream is given by 4/x.
Given that these times are equal, we can set up the following equation:
6/(x+3) = 4/x
Cross multiplying, we get:
6x = 4(x+3)
6x = 4x + 12
2x = 12
x = 6
Therefore, Alicia's rowing rate upstream is 6 miles/hour, and her rowing rate downstream is 6 + 3 = 9 miles/hour.
So, the correct answer is:
D. 9 mi/h downstream, 6 mi/h upstream.