How far did the farmer travel?...

Question

The cow was 6 miles ahead when the farmer started pursuing it. If the farmer, traveling at three times the cow's speed, took 1.25 hours to catch the cow, how far did the farmer travel?

(A) 13.25 miles

(B) 9.0 miles

(C) 7.25 miles

(D) 1.2 miles

(E) none of these

Answer 1

Let x be the cow's distance

Let y be the farmer's distance therefore we can write:

x miles+6 miles =y miles

Or the cow is 6 miles ahead of the farmer

Let x1 be the cows speed and y1 be the farmers speed. Knowing the acceleration of the farmer we can write this equation:

3*x1 = y1

We can now assume x = x1 and are both representative of the cow

Assume y=y1 and are representative of the farmer

To find how many miles traveled by the farmer we need both equations. First we need to solve for either x or y in one of the two equations.

3x = y

x+6=y

x=y-6 solved for x

Substitute this into the other equation

3*(y-6)=y

3y-18=y

-18=-2y

9=y

The farmer walked 9 miles to catch the cow

We can check our work by using the second equation again and plugging in our answer.

x+6=y

x+6=9

x=3

3x = y

3*3 =y

y=9

9=9

3x=9

x=3