A boat travels 28 km upstream in 7 hours. It travels 48 km downstream in 4 hours. Find the speed of the boat and the speed of the stream.

speed of boat in still water ---- x km/h

speed of current ------- y km/h

7(x-y) = 28 or
x - y = 4

4(x+y) = 48 or
x + y = 12

add them:
2x = 16
x = 8
in x+y=12, if x = 8 , y = 4

state the conclusion

To find the speed of the boat and the speed of the stream, we can set up a system of equations.

Let's assume the speed of the boat is B km/h and the speed of the stream is S km/h.

When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the stream. So, the speed of the boat relative to the ground when traveling upstream is (B - S) km/h.

Similarly, when the boat is traveling downstream (with the current), its effective speed is increased by the speed of the stream. So, the speed of the boat relative to the ground when traveling downstream is (B + S) km/h.

From the given information, we can write the following equations:

For the upstream journey:
(B - S) × 7 = 28

For the downstream journey:
(B + S) × 4 = 48

Now, let's solve these equations to find the values of B and S.

Equation 1: (B - S) × 7 = 28
Expand the equation: 7B - 7S = 28

Equation 2: (B + S) × 4 = 48
Expand the equation: 4B + 4S = 48

Now, we can solve this system of equations by using the method of elimination or substitution.

Multiply Equation 1 by 4 to match the coefficients of S:
28B - 28S = 112

Now, add Equation 2 and the modified Equation 1:
4B + 4S + 28B - 28S = 48 + 112
32B = 160
Divide both sides by 32:
B = 5

Now, substitute the value of B back into Equation 1 or 2 to find the value of S:

Using Equation 1: (B - S) × 7 = 28
(5 - S) × 7 = 28
35 - 7S = 28
-7S = 28 - 35
-7S = -7
Divide both sides by -7:
S = 1

Therefore, the speed of the boat is 5 km/h and the speed of the stream is 1 km/h.

To find the speed of the boat and the speed of the stream, we can use the concepts of relative speed and the formula for distance.

Let's assume the speed of the boat is represented by 'b' and the speed of the stream is represented by 's'.

When the boat is traveling upstream, the effective speed of the boat will be reduced by the speed of the stream. So, the relative speed of the boat while going upstream will be (b - s).

Similarly, when the boat is traveling downstream, the effective speed of the boat will be increased by the speed of the stream. So, the relative speed of the boat while going downstream will be (b + s).

We are given two scenarios:
1) The boat travels 28 km upstream in 7 hours.
2) The boat travels 48 km downstream in 4 hours.

Let's calculate the speed of the boat and the speed of the stream using these two scenarios.

Scenario 1:
Distance = Speed × Time
28 = (b - s) × 7

Scenario 2:
48 = (b + s) × 4

Now we have a system of two equations. Solving these equations will give us the values of 'b' (speed of the boat) and 's' (speed of the stream).

Let's solve the equations:

From Scenario 1:
28 = (b - s) × 7
Divide both sides by 7:
4 = b - s --(Equation 1)

From Scenario 2:
48 = (b + s) × 4
Divide both sides by 4:
12 = b + s --(Equation 2)

Now, we have a system of two equations. We can solve these equations simultaneously.

Adding Equation 1 and Equation 2:
(4 + 12) = (b - s) + (b + s)
16 = 2b
Divide both sides by 2:
b = 8

Substituting the value of 'b' in Equation 1:
4 = b - s
4 = 8 - s
Subtract 8 from both sides:
-4 = -s
Multiply both sides by -1:
4 = s

Therefore, the speed of the boat is 8 km/h and the speed of the stream is 4 km/h.