A boat can travel upstream 14 miles in same it can travel downstream 8 miles. the boat is traveling 13 miles per hour. what is the current
You have these reversed, faster downstream
speed upstream = 13 - v
speed downstream = 13 + v
time = distance/rate
14/(13+v)= 8/(13-v)
182 - 14 v = 104 + 8v
22 v = 78
v = 3.55 mph
check
speed downstream = 3.55+13 = 16.54
time downstream = 14/16.54 = .846 hr
speed upstream = 13 - 3.55 = 9.45
9.45 * .846 = 7.99 ok check
To find the speed of the current, we can use the concept of relative velocity.
Let's assume the speed of the boat in still water as B mph, and the speed of the current as C mph.
When the boat is traveling upstream, it has to overcome the current, so its effective speed will be B - C mph. Similarly, when the boat is traveling downstream, it gets a boost from the current, so its effective speed will be B + C mph.
Given that the boat can travel 14 miles upstream in the same time it can travel 8 miles downstream, we can set up the following equation:
Time taken to travel upstream = Time taken to travel downstream
14 / (B - C) = 8 / (B + C)
Cross multiplying, we get:
14(B + C) = 8(B - C)
Now, we are given that the boat is traveling at a constant speed of 13 mph, so we can substitute B = 13 into the equation:
14(13 + C) = 8(13 - C)
Simplifying the equation:
182 + 14C = 104 - 8C
Combining like terms:
22C = -78
Dividing both sides by 22:
C = -3.54
Since speed cannot be negative, we can ignore the negative sign and conclude that the speed of the current is approximately 3.54 mph.