A tugboat goes 160 miles up stream in 20 hours, return trip downstream takes 5 hours. Find speed of tugboat without the current and the speed of the current
distance = rate x time
In this case we have:
distance = (rate + current) x time
and
distance = (rate - current) x time
160 = 20(r-c)
160 = 5(r + c)
160 = 20r - 20c
160 = 5r + 5c
Can you solve from here?
To find the speed of the tugboat without the current (let's call it T) and the speed of the current (let's call it C), we can use the information given.
Let's first calculate the speed of the tugboat relative to the water when going upstream.
To do this, we use the formula:
Speed = Distance / Time
In this case, the distance is 160 miles and the time taken is 20 hours. So, the speed of the tugboat relative to the water when going upstream is 160 / 20 = 8 miles per hour (mph).
Now, let's calculate the speed of the tugboat relative to the water when going downstream.
Using the same formula, with a distance of 160 miles and a time of 5 hours, the speed of the tugboat relative to the water when going downstream is 160 / 5 = 32 mph.
Since the speed of the current affects the speed of the boat when going upstream and downstream, we can calculate it by finding the difference between the two speeds:
Speed downstream - Speed upstream = 32 - 8 = 24 mph.
So, the speed of the current is 24 mph.
To find the speed of the tugboat without the current, we can use the speed of the current and any one of the speeds obtained earlier:
Speed of the tugboat without current = Speed downstream - Speed of the current
= 32 - 24
= 8 mph.
Therefore, the speed of the tugboat without the current is 8 mph and the speed of the current is 24 mph.