A boat goes 24 km upstream and 28 km downstream in 6 hours . It goes 30 km…

Let x = speed of the boat in still water (km/hr) and y = speed of the stream (km/hr).

From the problem we get two equations for the total times:

• 24/(x - y) + 28/(x + y) = 6

• 30/(x - y) + 21/(x + y) = 6.5

To simplify, set a = 1/(x - y) and b = 1/(x + y). The equations become:

• 24a + 28b = 6

• 30a + 21b = 6.5

Solve this linear system by substitution.

• From 24a + 28b = 6, a = (6 - 28b)/24 = 1/4 - (7/6)b.

• Substitute into 30a + 21b = 6.5: 30(1/4 - (7/6)b) + 21b = 6.5.

• Compute: 7.5 - 35b + 21b = 6.5, so -14b = -1 and b = 1/14.

• Then a = 1/4 - (7/6)(1/14) = 1/4 - 1/12 = 1/6.

Now revert to x and y: x - y = 1/a = 6 and x + y = 1/b = 14. Solve these to get x = 10 and y = 4.

Answer: stream speed = 4 km/hr