The boat passed the river for 24 km in the same time as for 16 km against the river.

The boat passed the river for 24 km in the same time as for 16 km against the river. The boat’s own speed is exactly 12 km / h. Find the speed of the river.

Distance downstream (S downstream) = 24 km;

Distance upstream (Sp. Flow) = 16 km;

Time downstream (tпр. Flow.) = Time upstream (tпр. Flow.);

Boat speed (Vк.) = 12 km / h;

River flow speed (Vcurrent) -? km / h;

Because S = V * t, then:

S in flow = Vin flow. * t in flow, i.e. Vin flow * t flow = 24, so t in flow. = 24 / Vin flow;

Spr leak. = Vpr. tech. * t pr current, i.e. Vpr. tech. * t pr. current = 16, so t pr. Flow. = 16 / Vpr. tech .;

Speed ​​of the boat along the river:

Vin flow = Vk. + Vcur. = 12 + Vcurrent (km / h).

Speed ​​of the boat upstream of the river:

Vpr. tech. = Vk. – V leak. = 12 – Vcurrent (km / h).

Then we have:

t flow = 24 / Vin flow. = 24 / (12 + Vcurrent);

t pr. current = 16 / Vpr. tech. = 16 / (12 – Vcurrent).

Because by condition t downstream. = t pr. flow, then:

24 / (12 + Vflow) = 16 / (12 – Vflow);

24 (12 – Vflow) = 16 (12 + Vflow);

288 – 24V = 192 + 16V leak;

– 24V leak. – 16V leak. = 192 – 288;

-40V leak. = -96;

V leak. = 2.4 (km / h).

Answer: the speed of the river is 2.4 km / h.