a motorboat travels 9 miles downstream (with the current) in 30 minutes. the return trip upstream (against…

a motorboat travels 9 miles downstream (with the current) in 30 minutes. the return trip upstream (against the current) takes 90 minutes. which system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? recall the formula d = rt. 9 = 0.5(x - y) 9 = 1.5(x + y) 9 = 1.5(x - y) 9 = 0.5(x + y) 0.5 = 9(x - y) 1.5 = 9(x + y) 1.5 = 9(x - y) 0.5 = 9(x + y)

a motorboat travels 9 miles downstream (with the current) in 30 minutes. the return trip upstream (against the current) takes 90 minutes. which system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? recall the formula d = rt. 9 = 0.5(x - y) 9 = 1.5(x + y) 9 = 1.5(x - y) 9 = 0.5(x + y) 0.5 = 9(x - y) 1.5 = 9(x + y) 1.5 = 9(x - y) 0.5 = 9(x + y)

Answer

Explanation:

Step1: Convert time to hours

30 minutes = 0.5 hours, 90 minutes = 1.5 hours.

Step2: Find downstream speed - formula

Down - stream speed is the sum of boat speed and current speed. Using $d = rt$, when $d = 9$ miles and $t=0.5$ hours, $9 = 0.5(x + y)$ (where $x$ is boat speed and $y$ is current speed).

Step3: Find upstream speed - formula

Up - stream speed is the difference of boat speed and current speed. Using $d = rt$, when $d = 9$ miles and $t = 1.5$ hours, $9=1.5(x - y)$.

Answer:

$9 = 1.5(x - y)$ $9 = 0.5(x + y)$