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Mountain Bike Racer

Real-Life Activities

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.


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