Hello, MathLearner!

Here's #2 . . . a challenging problem!

2. A boat went down the river for a distance of 20 km.

It then turned back and returned to its starting point, having travelled a total of 7 hours.

On its return trip, at a distance of 12 km from the starting point, it encountered a log,

which had passed the starting point at the moment at which the boat had started downstream.

Find the downstream speed of the boat.

Let = speed of the boat in still water.

Let = speed of the current.

The boat went downstream for 20 km at a speed of km/hr.

. . This took: hours.

The boat went upstrream for 20 km at a speed of km/hr.

. . This took: hours.

The total trip took 7 hours: .

Consider when the boat met the log . . .

The boat had gone downstream 20 km at km/hr.

. . This took: hours.

Then the boat went upstream 8 km at km/hr.

. . This took: hours.

Total time: .

During this time, the log traveled 12 km at km/hr.

. . This took: .

Equate [1] and [2]: .

Then: .

Substitute into (a): .

. .

Substitute into [3]: .

Therefore, the downstream speed is: .