Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
The speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
Explanation:
Let's call x the speed of the boat and y the speed of the current.
The distance traveled is equal to the speed times the time, so the boat traveled 36 miles in three hours and we can write the following equation
(x + y)3 = 36
3(x + y) = 36
because when the boat traveled downstream, the total speed is the sum of x and y.
On the other hand, the boat traveled 30 miles upstream in 5 hours, so
(x - y)5 = 30
5(x - y) = 30
Therefore, the system of equations is
3(x + y) = 36
5(x - y) = 30
Solving the first equation for x, we get
[tex]\begin{gathered} 3(x+y)=36 \\ \\ \frac{3(x+y)}{3}=\frac{36}{3} \\ \\ x+y=12 \\ x+y-y=12-y \\ x=12-y \end{gathered}[/tex]Now, we can replace this expression on the second equation as follows
[tex]\begin{gathered} 5(x-y)=30 \\ \\ {\frac{5(x-y)}{5}}=\frac{30}{5} \\ \\ x-y=6 \\ \\ \text{ Replacing x = 12 - y} \\ 12-y-y=6 \\ 12-2y=6 \\ 12-2y-12=6-12 \\ -2y=-6 \\ \\ \frac{-2y}{-2}=\frac{-6}{-2} \\ \\ y=3 \end{gathered}[/tex]Then, the value of x is
x = 12 - y
x = 12 - 3
x = 9
So, the speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
