a motorboat moves 25 miles per hour in still water. it travels 21 miles upstream and 21 miles downstream in a total time of 2.0 hours. whatis the speed of the current?
time = distance/speed
21/(25+s) + 21/(25-s) = 2
s = 10
check:
21/35 + 21/15 = 2
To find the speed of the current, we need to set up equations based on the information given.
Let's assume the speed of the current is represented by "C" in miles per hour.
First, let's consider the boat's speed when it moves upstream (against the current). In this case, the boat's effective speed is reduced by the speed of the current. So, the relative speed of the boat moving upstream is (25 - C) miles per hour.
Similarly, when the boat moves downstream (with the current), the relative speed of the boat is increased by the speed of the current. So, the relative speed of the boat moving downstream is (25 + C) miles per hour.
Now, let's find the time taken when the boat travels upstream and downstream.
When the boat travels upstream for a distance of 21 miles at a relative speed of (25 - C) miles per hour, the time taken is given by:
Time upstream = Distance / Speed = 21 / (25 - C) hours
Similarly, when the boat travels downstream for a distance of 21 miles at a relative speed of (25 + C) miles per hour, the time taken is given by:
Time downstream = Distance / Speed = 21 / (25 + C) hours
According to the given information, the sum of the upstream and downstream times is 2.0 hours.
So, we can write the equation:
Time upstream + Time downstream = 2.0
Substituting the expressions for the times, we have:
21 / (25 - C) + 21 / (25 + C) = 2.0
To solve this equation for the speed of the current (C), we can cross multiply, combine terms, and solve for C.