The average round trip speed S in miles per hour of a vehicl

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.

Solution

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