To calculate: The speed of the woman
Her running speed is 3.78 mile/hour.
The distance she covers by cycling = 4 miles
The distance she covers by running= 2.5 miles
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)
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 quadratic equation:
Plug the numbers into the quadratic formula ,
From that, we get
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
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!
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