The car covered one tenth of the way at an average speed of 40 km / h, and the rest of the way at an

| August 22, 2021 | education

The car covered one tenth of the way at an average speed of 40 km / h, and the rest of the way at an average speed of 60 km / h. Find the average speed for the entire journey.

V1 = 40 km / h.

V2 = 60 km / h.

S1 = S / 10.

S2 = 9 * S / 10.

Vav -?

The average vehicle speed Vav is determined by the ratio of the total distance traveled S to the time of movement on this path t: Vav = S / t.

S2 = S – S1 = 10 * S / 10 – S / 10 = 9 * S / 10

The travel time along the entire path t will be determined by the formula: t = t1 + t2.

t1 = S1 / V1 = S / 10 * V1.

t2 = S2 / V2 = 9 * S / 10 * V2.

t = S / 10 * V1 + 9 * S / 10 * V2 = (S * V2 + 9 * S * V1) / 10 * V1 * V2 = S * (V2 + 9 * V1) / 10 * V1 * V2.

The formula for determining the average speed will be: Vav = S / S * (V2 + 9 * V1) / 10 * V1 * V2 = 10 * V1 * V2 / (V2 + 9 * V1).

Vav = 10 * 40 km / h * 60 km / h / (60 km / h + 9 * 40 km / h) = 57 km / h.

Answer: the average vehicle speed is Vav = 57 km / h.



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