MGMAT Eq/Ineq/Vics ed4 Chpt 7 #13

[aaronle3]

Chapter 7 #13.

Kate can run A feet in B seconds. Amelia can run C feet in D seconds. In a race of 1,000 feet, by how many seconds will Kate beat Amelia (assuming they both run at these rates)?

A) 1000(AD-BC)/(A)(C)
B) 1000(B)(C)-1000(D)(A)/AC
C) AB-CD/1000
D) AD-CB/1000

Here is what I understand so far:
Answers C&D are wrong because if we are looking for Time,
Time = Distance/Rate - so 1000 can not be in the denominator.

Now the answer key to this problem states that we need to use
T2 - T1. T2 being Amelia's time - T1 being Kate's time.

If it were T1-T2 we would get a negative value. So the answer from T2-T1 would give us how many more seconds it took Amelia to finish 1,000 ft race or how much less time it took Kate to beat Amelia.

So my question is:

1000D/C - 1000B/A = 1000(AD-BC)/AC

How would can I faster understand that the answer is manipulated and to see that answer A crosses out the variables to give the correct answer? Please tell me the answer is not to do more problems......

[tim]

doing more problems won't help until you've got the concept down. your first step is to go back and review your rules for adding and subtracting fractions - learn how to find a common denominator and you'll see that the correct answer follows immediately just from the process of subtracting the fractions..

[tim]

if you're gonna spam our forums, at least make it coherent!