Your average speed on the first half of a car trip is 700 km

Your average speed on the first half of a car trip is 70.0 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?

Solution

1st Half DATA:
distance = x km ; rate = 70 km/h ; time = d/r = x/70 hrs.
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2nd Half DATA:
distance = x km ; rate = r km/h ; time = x/r hrs.
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Total Trip DATA:
distance = 2x km; rate = 85 km/h ; time = (2x)/85 hrs
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Equation:
time + time = total time
x/70 + x/r = (2x)/85
1/70 + 1/r = 2/85
(r+70)/70r = 2/85
Cross-Multiply:
140r = 85r + 85*70
55r = 85*70
r = 108.18 kph (rate needed in the 2nd half of the trip)