the average round trip speed S in miles per hour of a vehicle traveling a distan

Question

the average round trip speed S in miles per hour of a vehicle traveling a distance of d miles in each direction is given by

where r1and r2 are the rates of the speed for the initial trip and the return trip respectively. Suppose a motorist travels 200 miles to an event and averages 50 mph for the trip of the event. Determine the average speed necessary for the return trip if the motorist wants the average speed for the round trip to be at least 55 mph. Round to one decimal place. Write a sentence that explains your result.

Explanation / Answer

S = 2d/(d/r1 + d/r2)

d = 200 miles ; d/r1 = 50 mph ( to the event) ; S = 55 mph (atleast)

S>55 mph

So, 2*200/(200/50 +200/r2) > 55

2/(1/50 + 1/r2) > 55

1/50 +1/r2 < 2/55

1/r2 < 2/55 - 1/50

1/r2 < 0.016

r2 > 62.5 mph So, avg speed on return must be greater than 62.5 mph to achieve the avg round trip speed of 55 mph

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