A woman cycles 8 mi/hr faster than she runs. Every morning she cycles 4 mi and runs 2 1/2 mi, for a total of one hour of exercise. How fast does she run?
1 Answer
We need to figure out how much time she spends cycling and walking each morning, then figure how her speed from that
Explanation:
Let's get this into a more math-y format. First of all, we want to know her running speed. Let's call that
Let's call her cycling speed
So, she cycles for 4 miles, and runs for 2.5 miles
4 miles
2.5 miles
We know that this whole process takes 1 hour:
Get rid of those fractions by multiplying both sides by
From the question, we know that her cycling speed is 8 miles / hour faster than her running speed. So, we can say that
Let's replace
Combine like terms:
And get this into the form of a quadratic equation:
Plug our numbers into the quadratic formula, which is
Where
From that, we find that
OR
We know that this woman cannot run -5.28 miles per hour (she can't run at a negative speed), so
her running speed (
Let's check:
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!