River Current A boat can travel 36 miles upstream in the same time that it can travel 54 miles downstream. If the speed of the current is 3 miles per hour, find the speed of the boat without a current.
let speed of boat in still water be x mph
upstream:
speed = x-5
time = 36/(x-5)
downstream:
speed = x+5
time = 54/(x+5)
the two times are equal, so
36/(x-5) = 54(x+5)
54x - 270 = 36x + 180
18x = 450
x = 25
The speed of the boat without a current is 25 mph
A canoe can travel 18 mph in still water and 22 miles downstream in the same amount of time that it takes to travel 14 mph upstream. Find the speed of the current in the water.
a person can copy the final exam in 28 minutes using a new copy machine. using an old copy machine, it takes 70 minutes. if both machines are used, how long will it take to complete the job
To find the speed of the boat without a current, we can set up a system of equations based on the given information.
Let's assume that the speed of the boat without a current (also known as the boat's speed in still water) is represented by "b" (in miles per hour).
When the boat is traveling upstream (against the current), its effective speed is reduced due to the current. The speed of the current is 3 miles per hour, so the boat's effective speed becomes (b - 3) miles per hour.
Similarly, when the boat is traveling downstream (with the current), its effective speed is increased due to the current. Therefore, the effective speed downstream is (b + 3) miles per hour.
Now, we are given that the boat can travel 36 miles upstream in the same time it takes to travel 54 miles downstream. Let's use the formula:
Time = Distance / Speed
So, the time taken to travel 36 miles upstream is given by:
Time upstream = 36 / (b - 3)
And the time taken to travel 54 miles downstream is given by:
Time downstream = 54 / (b + 3)
Since we are told that these two times are equal, we can set up the following equation:
36 / (b - 3) = 54 / (b + 3)
To solve this equation, we can cross-multiply:
36 * (b + 3) = 54 * (b - 3)
Expanding both sides of the equation:
36b + 108 = 54b - 162
Bringing like terms to one side:
18b = 270
Dividing both sides by 18:
b = 270 / 18
Simplifying:
b = 15
Therefore, the speed of the boat without a current is 15 miles per hour.