catty2004 wrote:
Thanks for the explanation, but im not sure why using 25 -12 = 13 is equivalent of approximating car Y's distance traveled??
Responding to a pm:
Notice what it is given to you:
Car X runs 25 miles in 1 gallon of fuel.
Car Y runs approx 12 miles in 1 gallon of fuel (since options are not close to each other, we can easily approximate 11.9 to 12. If options are very close to each other, you need to calculate a more accurate answer)
So Car X runs an extra 13 miles in one gallon of fuel.
Now what does the term 12000/13 represent? Is it the extra fuel used by car Y? No. This will be the fuel used by a car which runs 12000 miles at an average of 13 miles in one gallon. But neither car X nor car Y does that.
Car X needs 12000/25 = 480 gallons of fuel
Car Y needs 12000/12 = 1000 gallons of fuel
What we need to do here is \(\frac{12000}{12} - \frac{12000}{25}\). I hope this is obvious to you that this is not equal to \(\frac{12000}{(25 - 12)}\)
When the denominators are different, we cannot combine the fractions. We can combine them in case the denominators are the same. Since 25 and 12 are in the denominator of the quantity we need, we cannot combine them.