Real-Life Math -- Solution
Here's the breakdown of the track:
35 percent
is dedicated to corners
45 percent of it is straight
20 percent of
it makes up the exit of the turn
First you need to figure
out the length of each section of the course.
35 percent
of 5 km = 1.75 km
45 percent of 5 km = 2.25 km
20 percent of 5 km
= 1 km
Now you need to figure out your total time
around the course on the heavier tires compared to the lighter tires.
Heavier
Tires
Time = Distance / Speed
Corner
time = 1.75 km / 20 km/hr
Corner time = 0.09 hr
Straightaway
time = 2.25 km / 40 km/hr
Straightaway time = 0.06 hr
Turn
exit time = 1 km / 25 km/hr
Turn exit time = 0.04 hr
Total
time of the course with heavy tires:
Total time = 0.09
hr + 0.05 hr + 0.04 hr
Total time = 0.18 hr
Convert
to minutes:
0.18 hr x 60 minutes per hour = 10.8 minutes
It
will take you an estimated 10.8 minutes to complete the course with the heavy
tires.
Lighter Tires
Corner time = 1.75
km / (22 km/hr - 6 km/hr)
Corner time = 1.75 km / 16 km/hr
Corner
time = 0.11 hr
Straightaway time = 2.25 km / 45 km/hr
Straightaway
time = 0.05 hr
Turn exit time = 1 km / (25 km/hr - 5 km/hr)
Turn
exit time = 1 km / 20 km/hr
Turn exit time = 0.05 hr
Total
time of the course with light tires:
Total time = 0.11
hr + 0.05 hr + 0.05 hr
Total time = 0.21 hr
Convert
to minutes:
0.21 hr x 60 minutes per hour = 12.6 minutes
It
will take you an estimated 12.6 minutes to complete the course with the light
tires. According to your calculations, it will take you about 2 minutes longer
to complete the course with lighter tires -- a time that could mean winning
or losing the race. You decide to go with the heavier tires.