Determine the average speed of the boat along the way. If she: 1) swam at the speed v1 = 4.0 km / h

Determine the average speed of the boat along the way. If she: 1) swam at the speed v1 = 4.0 km / h for the first quarter of the time, the rest of the time – at the speed v2 = 8.0 km / h; 2) the first quarter of the way swam at a speed of v1 = 4.0 km / h, the rest of the way – at a speed of v2 = 8.0 km / h.

Option A:

Given:

v1 = 4.0 km / h – boat speed during t / 4;

v2 = 8.0 km / h – boat speed during 3 * t / 4.

It is required to find the average speed of the boat along the entire path Vav (km / h).

Vav = S total / t total = (S1 + S2) / t = (v1 * t / 4 + v2 * 3 * t / 4) / t = t / 4 * (v1 + 3 * v2) / t = (v1 + 3 * v2) / 4 = (4 + 3 * 8) / 4 = (4 + 24) / 4 = 28/4 = 7 km / h.

Answer: the average speed along the entire route is 7 km / h.

Option B:

v1 = 4.0 km / h – boat speed beyond the S / 4 section;

v2 = 8.0 km / h – boat speed for the section 3 * S / 4.

It is required to find the average speed of the boat along the entire path Vav (km / h).

Vav = S total / t total = S / (t1 + t2) = S / (S / 4 * v1 + 3 * S / 4 * v2) = 4 * S * v1 * v2 / S * (v2 + 3 * v1) = 4 * v1 * v2 / (v2 + 3 * v1) = 4 * 4 * 8 / (8 + 3 * 4) = 128 / (8 + 12) = 128/20 = 6.4 km / h.

Answer: The average speed along the entire route is 6.4 km / h.