Thread: Applying Cramer's Rule to Word Problems

1. Applying Cramer's Rule to Word Problems

I've spent all weekend trying to figure this out, and I believe I'm overthinking the problem and the answer might be staring me in the face.

My instructions for the following word problem are to set up an appropriate system of two linear equations in two unknowns and then solve the system by determinants.

The problem is:

Two joggers are 2.0 mi apart. If they jog toward each other, they will meet in 12 minutes. If they jog in the same direction, the faster one will overtake the slower one in 2.0 hours. At what rate does each jog?

I am not necessarily looking for the final answer to this problem, I'd just like some help on how the two equations should be set up. Especially regarding jogging in the same direction using only two unknowns.

2. A is 2mi away from B

Let r = rate of A
And s = rate of B
And, say, r is faster than s.

Be consistent with units.
units for distance is mi.
units for time is hr.
units for rate in mi/hr.
So, 12 minutes = 12/60 = 1/5 hr

distance = rate * time

They jog toward each other
r(1/5) +s(1/5) = 2
So,
r +s = 10 -------------(1)

They jog in the same direction
(distance traveled by A) = (2 mi. + distance traveled by B)
r(2.0) = 2 +s(2.0)
2r = 2 +2s
r = 1 +s
r -s = 1 ---------(2)

3. It seems so simple now!

I was confusing myself by trying to convert hours into minutes first, instead of vice versa.

Thank you!