tana rode a boat 1 km upstream in and hour. rowing at the same rate, she made the return trip downstream in 15 minutes. find the rate of the current
tana's rate -- x km/h
current rate -- y km/h
1(x-y) = 1
(1/4)(x + y) = 1 or x+y = 4
add them
2x = 5
x = 5/2
then y = 3/2
rate of current is 1.5 km/h
let v be her rowing velocity in still water, r be the velocity of the water.
1km=(v-r)*1hr
1km=(v+r)*.25hr
multipy the second equation by 4
4km=(v+r)1
now add the equations..
5km=2v and you have v = 2.5km/hr
so r must be 1.5km/hr (see equation 1)
To find the rate of the current, we can analyze the given information and use a basic equation of motion. Let's denote the boat's speed in still water as x, and the rate of the current as y.
When Tana is travelling upstream, she is rowing against the current, so her effective speed is reduced. In this case, her speed (x) minus the current's speed (y) is equal to the distance covered in a given time (1 km in 1 hour). Mathematically, we can express this as:
x - y = 1/1 (Equation 1)
When Tana is going downstream, she is aided by the current, which increases her effective speed. In this case, her speed (x) plus the current's speed (y) is equal to the distance covered in a given time (1 km in 15 minutes, which is 1/4 of an hour). Mathematically, we can express this as:
x + y = 1/(1/4) (Equation 2)
To solve this system of equations, we can use the method of substitution. By rearranging Equation 1 to solve for x, we get:
x = 1 + y (Equation 3)
Substituting Equation 3 into Equation 2, we have:
1 + y + y = 4
Combining like terms:
2y + 1 = 4
Subtracting 1 from both sides:
2y = 3
Dividing both sides by 2:
y = 3/2
Therefore, the rate of the current is 3/2 km/hour.