Concept explainers
To calculate: The speed of the woman
Answer to Problem 83RE
Her running speed is 3.78 mile/hour.
Explanation of Solution
Given information:
The distance she covers by cycling = 4 miles
The distance she covers by running= 2.5 miles
Formula used:
First of all, we want to know her running speed. Let's call that x
x = running speed (miles / hour)
Let's call her cycling speed y...
y = cycling speed (miles / hour)
So, she cycles for 4 miles, and runs for 2.5 miles
4 miles ÷y miles / hour is how long it takes her to cycle for 4 miles
2.5 miles ÷x miles / hour is how long it takes her to run for 2.5 miles
Since this whole process takes 1 hour:
Get rid of those fractions by multiplying both sides by (x)(y)
Calculation:
From the question, we know that her cycling speed is 8 miles / hour faster than her running speed. So, we can say that
Replace y in our equation, then:
Combine like terms:
And get this into the form of a
Plug the numbers into the quadratic formula ,
Where
From that, we get
OR
As this woman cannot run -5.28 miles per hour ( negative speed), so her running speed (x) must be 3.78 miles/hour, and her cycling speed (8 miles/hour faster) is 11.78 miles/hour
Verification:
2.5 miles, at 3.78 miles/hour would take 0.661 hours
4 miles, at 11.78 miles/hour would take 0.339 hours
For a total of 1 hour!
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning