Problems - Units of Measurement

Question 1:
In a recent Tour de France time trial, Lance Armstrong traveled 31 mi in a time trial in 1h 4min.
What was his average speed in mph?

Solution 1:
d = 31 mi ; t = 1h 4min ; v = ? mph
v = d/t = 31 mi / (1h 4min )
   = 31 mi / (1h + (4min x  1 h/60min))
   = 31 / (1 + (4/60)) mi/h
   = 29.0625 mph
   = 29.06 mph


Question 2:
A pitcher has the ability to throw a baseball at 95 mph.
a. How fast is the speed in ft/s?
b. How long does the hitter have to make a decision about swinging at the ball if the plate and the mound are seprated by 60 ft?
c. If the batter wanted a full second to make a decision, what would the speed in mph have to be?
Solution 2:
v = 95 mph
a. v = ? ft/s
v = 95 mph
   = 95 mi/h * (5280 ft/1 mi) * (1 h/ 3600 s)
   = (95 * 5280 / 3600) ft/s
   = 139.33 ft/s

b. d = 60 ft ; t =? s
t = d / v
   = 60 ft / 139.33 ft/s
   = 60/139.33 s
   = 0.431 s

c. d = 60 ft ; t =1 s ; v = ? mph
v = d / t
   = 60 ft / 1 s * (1 mi/ 5280 ft) * (3600 s/ 1h)
   = 60 / 5280 * 3600 mi/h
   = 40.91 mph