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Length of the whole trip = D km

Unknown speed for the second half = X km/hr

Time for the first half = (D/2)/67 = D/134 hours

Time for the second half = (D/2)/x = D/(2x) hours

Total time for the trip = (D/134) + (D/2x) = D/86

1/134 + 1/2x = 1/86

2x/134 + 1 = 2x/86

x/67 + 1 = x/43

x(1/43 - 1/67) = 1

x = 1 / (1/43 - 1/67) = (43 x 67) / (67 - 43) = 2881/24 = 120.042 km/hr (rounded)

=============================================

Check:

(1/134) + (1/240.084) = (240.084 + 134) / (240.084 x 134) = 1/86 QED yay !

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Q: What if your average speed on the first half of a car trip is 67 km per hour How fast do you have to drive on the second half of the trip to achieve an average speed of 86 km per ho for the whole trip?
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