Question

a rowing team rowed 60 miles while going with the current in the same amount of time as it took to row 30 miles going against the current. the rate of the current was 3 miles per hour. find the rate of the rowing team in still water. rate of the team in still water: miles/hour

Explanation:

Step1: Define variables

Let \( r \) be the rate of the rowing team in still water (in miles per hour). The rate with the current is \( r + 3 \) (since the current helps), and the rate against the current is \( r - 3 \) (since the current opposes).

Step2: Set up time equations

Time \( t=\frac{\text{distance}}{\text{rate}} \). Time with current: \( t_1=\frac{60}{r + 3} \). Time against current: \( t_2=\frac{30}{r - 3} \). Since times are equal, \( \frac{60}{r + 3}=\frac{30}{r - 3} \).

Step3: Solve the equation

Cross - multiply: \( 60(r - 3)=30(r + 3) \).
Expand: \( 60r-180 = 30r + 90 \).
Subtract \( 30r \) from both sides: \( 30r-180 = 90 \).
Add 180 to both sides: \( 30r=270 \).
Divide by 30: \( r = 9 \).

Answer:

9