Final answer:
To find Kyle’s upstream and downstream speeds, we set up a system of equations based on the given information. Solving these equations, we find that Kyle’s downstream speed is 5 mph and his upstream speed is 3 mph.
Step-by-step explanation:
To find Kyle's upstream and downstream speeds, we can set up a system of equations based on the given information.
Let's say Kyle's speed going downstream is x miles per hour. This means his speed going upstream is x - 2 miles per hour, as stated in the question.
Now, let's use the concept of speed = distance/time to form our equations:
- When rowing upstream, Kyle covers a certain distance in 50 minutes, which is 50/60 = 5/6 hours. So, his speed going upstream is (distance)/(time) = (distance)/((5/6)) = 6(distance)/5 = (x - 2) miles per hour.
- When rowing downstream, Kyle covers the same distance in 30 minutes, which is 30/60 = 1/2 hours. So, his speed going downstream is (distance)/(time) = (distance)/((1/2)) = 2(distance) miles per hour.
Now we have two equations:
- (x - 2) = 6(distance)/5
- 2(distance) = x
We can solve these equations simultaneously to find the values of x and the distance. Let's solve equation 1 for distance:
- Since (x - 2) = 6(distance)/5, we can rearrange it to (x - 2) x (5/6) = distance.
Now, plug this value of distance into equation 2 and solve for x:
- Using the value of distance from equation 3 in equation 2, we get 2((x - 2) x (5/6)) = x.
- Simplifying this equation, we have 10(x - 2) = 6x.
- Expanding and rearranging, we get 10x - 20 = 6x.
- Combining like terms, we have 4x - 20 = 0.
- Adding 20 to both sides, we get 4x = 20.
- Dividing by 4, we get x = 5.
Now that we have found x, which represents Kyle's speed going downstream, we can substitute it back into equation 2 to find the distance:
- (2 x distance) = 5.
- Simplifying, we get distance = 5/2 = 2.5 miles.
Therefore, Kyle's downstream speed is 5 miles per hour and his upstream speed is 3 miles per hour.