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

Given that

avearge speed S = 55 mph

r1 = 50 mph

r2 = ?

Since he travelled equal distance in each direction,

Avearge speed S = 2r1r2/ (r1+r2)

55 = 2 x 50x r2 / ( 50+ r2)

2750 + 55 r2 = 100 r2

45 r2 = 2750

r2 = 2750/45

= 61.11 mph

r2 = 61.11 mph

Therefore,

average speed necessary for the return trip =  61.11 mph

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