A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes and the return trip takes 15 minutes. What is the speed of the current?
at what speed does current is in relative to water
let spped of current be X, when the boat goes upstream, the actual speed of boat= speed of boat-speed of current;when the boat goes downstream, the speed =speed of boat+speed of current
distance=speed x time
upstream: (16-X)x 1/3
downstream:(16+X)x1/4
since the total distance of the trip doesnt change,
(16-X)x 1/3=(16+X)x1/4
solve for x,
ps:the speed of boat is 16miles/hour,
dont forget to convert minutes into hour
To find the speed of the current, we can use the concept of relative motion. Let's denote the speed of the current as 'c' and the speed of the boat in still water as 'b'.
On the upstream trip, the boat is moving against the current, so the effective speed will be the difference between the boat's speed and the current's speed:
Effective speed upstream = b - c
On the downstream trip, the boat is moving with the current, so the effective speed will be the sum of the boat's speed and the current's speed:
Effective speed downstream = b + c
Given that the boat's constant speed relative to the water is 16 miles per hour, we can express these speeds as:
Effective speed upstream = 16 - c
Effective speed downstream = 16 + c
Now, let's convert the time taken for the trips to hours. The upstream trip takes 20 minutes, which is 20/60 = 1/3 hour, while the downstream trip takes 15 minutes, which is 15/60 = 1/4 hour.
We know that the distance traveled in each direction is the same since it's from and back to the same point.
Using the formula distance = speed × time, we can equate the distances of the upstream and downstream trips:
Distance upstream = Distance downstream
(speed upstream) × (time upstream) = (speed downstream) × (time downstream)
(16 - c) × (1/3) = (16 + c) × (1/4)
Now, we can solve this equation to find the value of 'c', the speed of the current.