a motorboat can maintain a constant speed of 11 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 21 minutes; the return trip takes 1 minutes. That is the speed of the current?
To find the speed of the current, we need to use the concept of relative motion.
Let's assume that the speed of the current is "c" miles per hour.
When the boat is moving upstream (against the current), it has to overcome the speed of the current. Hence, the effective speed of the boat will be the speed of the boat minus the speed of the current, i.e., (11 - c) miles per hour.
When the boat is moving downstream (with the current), the current aids the boat's movement. Hence, the effective speed of the boat will be the speed of the boat plus the speed of the current, i.e., (11 + c) miles per hour.
Now, let's calculate the distances covered in each case:
Distance upstream = Speed upstream × Time upstream
Distance upstream = (11 - c) × (21/60) miles
Distance downstream = Speed downstream × Time downstream
Distance downstream = (11 + c) × (1/60) miles
Now, the distance covered upstream and downstream is the same, as the boat travels to the same point and returns back.
Setting up the equation: Distance upstream = Distance downstream
(11 - c) × (21/60) = (11 + c) × (1/60)
To solve the equation, let's simplify it step by step:
(11 - c) × (21/60) = (11 + c) × (1/60)
11 - c = (11 + c) × (1/3) <-- Cross-multiplying
11 - c = (11 + c)/3
33 - 3c = 11 + c <-- Multiplying both sides by 3 to get rid of the denominator
33 - 11 = c + 3c
22 = 4c
c = 22/4
c = 5.5
Hence, the speed of the current is 5.5 miles per hour.
PsyDAG answered the same question here
http://www.jiskha.com/display.cgi?id=1276112108
Just change the numbers to fit your problem.