Physics average speed qusetion pls help :)?

Question

Your average speed on the first half of a car trip is 74.0 km/h. How fast do you have to drive on the second half of the trip to achieve an average speed of 85.0 km/h for the whole trip?

can someone pls explain this oen to me?

thankss youuss :)!

Answer 1

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distance = (rate)(time)

For the first half of the trip:

x/2 = (74.0 km/h)(t1)

t1 = x/(2 * 74.0 km/h) [1]

For the second half:

x/2 = (v)(t2)

t2 = x/(2v) [2]

For the whole trip:

x = (85.0 km/h)(t1 + t2) [3]

Adding [1] & [2], substitute into [3], and solve for v:

t1 + t2 = x/(2 * 74.0 km/h) + x/(2v)

x = (85.0 km/h)(x/(2 * 74.0 km/h) + x/(2v))

1 = (85.0 km/h)(1/(2 * 74.0 km/h) + 1/(2v))

1/(85.0 km/h) - 1/(2 * 74.0 km/h) = 1/(2v)

(85.0 km/h)(74.0 km/h) / [(2 * 74.0 km/h) - (85.0 km/h)] = v

v = 99.8 km/h