The distance from A to B is how many yards?

Question

Jill ran around the track four times for a total of 1000 yards. The track distance from A to B is

the same as the distance from C to D. The distance from B to C is the same as the distance from

D to A. The distance from C to D is 25 more yards than the distance from D to A. The distance

from A to B is how many yards?

Answer 1

We get the following from the word problem. (The track is a rectangle with point A-B-C-D)

4*(AB+BC+CD+AD) = 1000

AB = CD = 25 + AD

BC = AD

plug in the 2nd & 3rd equations into the 1st equation

4*(AB+BC+CD+AD) = 1000

4*((25 + AD)+AD+(25 + AD)+AD) = 1000

4*(50+4*AD) = 1000

200+16*AD = 1000

16*AD = 800

AD = 50

BC = AD = 50

Now plug that into your 2nd equation to find AB & CD

AB = CD = 25 + AD

AB = CD = 25 + 50

AB = CD = 75

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Always check your work!

4*(AB+BC+CD+AD) = 1000

4*(75 + 50 + 75 + 50) 1000

4*250 = 1000

1000 = 1000 CORRECT!

AB = CD = 25 + AD

75 = 75 = 25 + 50

75 = 75 = 75 CORRECT!