step 1
Find the circumference of the wheels
we know that
C=2(pi)(r)
we have
r=24/2=12 in -----> the radius is half the diameter
C=2(pi)(12)
C=24(pi) in
step 2
we have that
The wheels are turning at 455 rpm
rpm is revolution per minute
one revolution represent one circumference of the wheels
so
455(24(pi))=10,920 (pi) in per minute
assume
pi=3.14
substitute
10,920(3.14)=34,288.8 in per minute ------> linear speed
we need to convert to mph
so
miles per hour
34,288.8 inches/minute
we have that
1 mile=63360 inches
so
34,288.8 inches=34,288.8/63360=0.54117 miles/minute
Convert minutes to hours
1 hour =60 minutes
so
0.54117 miles/minute=0.54117(60)=32.47 mph
therefore
'the linear speed is 32.47 mph