The cyclist traveled a third of the way at a speed of 16 km / h; half of the remaining time – at a speed of 10 km / h

| March 8, 2021 | education

The cyclist traveled a third of the way at a speed of 16 km / h; half of the remaining time – at a speed of 10 km / h, and the last section – went at a speed of 6 km / h. What is its average speed all the way?

V1 = 16 km / h.

V2 = 10 km / h.

V3 = 6 km / h.

S1 = S / 3.

t2 = t3.

S1 = S2 + S3.

Vav -?

Vav = S / t.

t = t1 + t2 + t3.

t1 = S1 / V1 = S / 3 * V1.

t2 = S2 / V2, t3 = S3 / V3.

S2 / V2 = S3 / V3.

S2 / 10 = S3 / 6.

S3 = 6 * S2 / 10 = 3 * S2 / 5.

S1 = S2 + S3.

S = S1 + S2 + S3 = 2 * (S2 + S3) = 2 * (S2 + 3 * S2 / 5) = 16 * S2 / 5.

t1 = 16 * S2 / 3 * 5 * V1 = 16 * S2 / 15 * V1 = 16 * S2 / 15 * 16 = S2 / 15.

t2 = S2 / V2 = S2 / 10.

t3 = 3 * S2 / 5 * V3 = 3 * S2 / 5 * 6 = S2 / 10.

t1 + t2 + t3 = S2 / 15 + S2 / 10 + S2 / 10 = 8 * S2 / 30 = 4 * S2 / 15.

Vav = S / t = (16 * S2 / 5): (4 * S2 / 15) = 12 km / h.

Answer: the average speed of the cyclist was Vav = 12 km / h.



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