A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers…

Let the speed of the boat in still water be b km/hr and the speed of the stream be s km/hr.

Then upstream speed = b - s and downstream speed = b + s. From the problem we get two equations for total times:

• 32/(b - s) + 36/(b + s) = 7

• 40/(b - s) + 48/(b + s) = 9

Let x = b - s and y = b + s. Then we have a linear system in 1/x and 1/y. Set u = 1/x and v = 1/y to get:

• 32u + 36v = 7

• 40u + 48v = 9

Solve this linear system. Using elimination (or Cramer's rule) yields u = 1/8 and v = 1/12, so x = 8 km/hr and y = 12 km/hr.

Now recover b and s:

• b = (x + y)/2 = (8 + 12)/2 = 10 km/hr

• s = (y - x)/2 = (12 - 8)/2 = 2 km/hr

Check: For the first journey 32/8 + 36/12 = 4 + 3 = 7 hours; for the second 40/8 + 48/12 = 5 + 4 = 9 hours. Both match the given times.

Answer: boat speed in still water = 10 km/hr; speed of the stream = 2 km/hr.