In algebra right now, we're doing inverses and stuff. And I'm not sure if this problem can be solved with using an inverse formular, or just solved regularly....

Brian is rowing in a marathon. When rowing downstream, he is traveling at a rate of 10 miles per hour. While he rests, he travels downstream at a rate of 3 miles per hour. He rows for an hour and rests for an hour.

A. If he continues this pattern, how many hors will it take him to travel 182 miles?

B. What is his average speed per hour?

I really appreciate a little help, or a lot of help. Anything you know about this, help me out!! THANK YOUUU!!

Since Brian travels 13 miles in two hours, he averages 6.5 miles per hour. Divide 182 by 6.5 to find how many hours it will take him.

We'll be glad to check your work.

thank you. :]

To solve this problem, we can divide it into two parts: the time Brian spends rowing and the time he spends resting.

A. To find out how many hours it will take Brian to travel 182 miles, we need to calculate the time spent rowing and the time spent resting separately.

Let's start with the time spent rowing. We know that Brian rows at a rate of 10 miles per hour. Therefore, for every hour he rows, he covers 10 miles.

To find the time spent rowing, we divide the total distance (182 miles) by the rowing rate (10 miles per hour):

Time rowing = Distance / Rate = 182 miles / 10 miles per hour = 18.2 hours

So, Brian will spend 18.2 hours rowing.

Next, let's calculate the time spent resting. We know that while resting, he travels downstream at a rate of 3 miles per hour. Therefore, for every hour he rests, he covers 3 miles.

To find the time spent resting, we divide the total distance (182 miles) by the resting rate (3 miles per hour):

Time resting = Distance / Rate = 182 miles / 3 miles per hour = 60.67 hours

However, we need to keep in mind that Brian rests for 1 hour after each hour of rowing. Therefore, we need to adjust the time spent resting by subtracting the number of resting periods (which is the same as the number of hours spent rowing).

Adjusted time resting = Time resting - Time rowing = 60.67 hours - 18.2 hours = 42.47 hours

Now, to find the total time Brian will take to travel 182 miles, we add the time spent rowing and the adjusted time spent resting:

Total time = Time rowing + Adjusted time resting = 18.2 hours + 42.47 hours = 60.67 hours

So, Brian will take approximately 60.67 hours to travel 182 miles.

B. To find his average speed per hour, we divide the total distance (182 miles) by the total time taken (60.67 hours):

Average speed = Distance / Time = 182 miles / 60.67 hours ≈ 2.997 miles per hour

Therefore, Brian's average speed per hour is approximately 2.997 miles per hour.

In conclusion, it will take Brian about 60.67 hours to travel 182 miles, and his average speed per hour is approximately 2.997 miles per hour.