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# Calculus: Lower and Upper Estimates

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Roger decides to run the marathon. His friend follows in a car and clocks his speed in mph. Roger stops after an hour and a half but his friend keeps the following records:

1. Calculate upper and lower estimates for the distance the two have traveled from the starting gate.
2. If he started at 8am could Roger have walked to the finish line before night fall or should he take a ride with his friend?

https://brainmass.com/math/calculus-and-analysis/calculus-lower-upper-estimates-444524

#### Solution Preview

A step by step detailed solution is attached.

Solution:
Step 1: Convert time from minutes to hours
Step 2: Compute distance travelled using the following formula:
Distance = Speed (miles) x Time (hours)
Time (h) 0 15/60 = 0.25 30/60 = 0.5 45/60= 0.75 60/60 = 1.00 75/60= 1.25 90/60 = 1.50
Speed (mph) 10 10 9 9 8 8 7

To find lower estimate, you need to use Right Hand Sum ...

#### Solution Summary

Roger decides to run the marathon. His friend follows in a car and clocks his speed in mph. Roger stops after an hour and a half but his friend keeps the following records:

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