The average round trip speed S in mph of a vehicle traveling

The average round trip speed S (in mph) of a vehicle traveling a distance of d miles in each direction is given by

A. Suppose that a motorist travels 200 mi from her home to an athletic event and averages 50 mph for the trip to the event. Determine the speeds necessary if the motorist wants the average speed for the round trip to be at least 60 mph?

B. Would the motorist be traveling within the speed limit of 70 mph?

Solution

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

d/r1 =200/ 50 mph = 4 mph ; d/r2 = x ; S = 60 mph ; d= 200mi

Pulgging the values in the formula:

60 = 2*200/( 4+x)

4+x = 400/60

x= 6.67- 4= 2.67 hr

So, speed while return = 200/2.67 = 74.9 mph\\

B) No, he crosses the speed limit of 70mph