How long does it take each to run five miles?

Question

It takes ms. Fittereer 15 more minutes to run five miles than it takes Ms. Heslin. Twice Ms. Heslins time is 15 more mintues than Ms. Fitter's. How long does it take each to run five miles?

Answer 1

Let F = Ms. Fittereer's time in minutes.
Let H = Ms. Heslin's time in minutes.

"It takes Ms Fittereer 15 more minutes than it takes Ms. Heslin" In other words "Ms. Fittereer's time is Ms. Heslin's time plus 15 minutes"
F = H + 15

"Twice Ms. Heslin's time is 15 minutes more than Ms. Fitter's"
2H = F + 15

So substitute for F in the second equation:
2H = (H + 15) + 15

Simplify:
2H = H + 30

Subtract H from both sides:
H = 30

Now solve for F, by substituting H back into equation #1:
F = H + 15
F = 30 + 15
F = 45

So Ms. Fittereer takes 45 minutes and Ms. Heslin takes 30 minutes.

The distance doesn't really matter in this case (unless you needed to figure out speed). By the way, Ms. F runs 6 2/3 miles an hour and Ms. H runs 10 miles an hour.

Your answer is:
Ms. Fittereer = 45 minutes
Ms. Heslin = 30 minutes

Answer 2

If:
Y=Ms.Fittereer
X=Ms.Heslin

Then you have two equations:
x+15=y
2x=y+15

Now Solve:
x=y-15
2(y-15)=y+15
2y-30=y+15
+30 +30
2y=y+45
-y -y
y=45
x=45-15
x=30

Answer:
Ms.Fittereer runs 5 miles in 45 min.
Ms.Heslins runs 5 miles in 30 min.

Answer 3

let F take x min and H take y minutes
the equations are
x-y=15
2y-x=15
adding y=30 and substituting x=45
F takes 45 min and H takes 30 min