SOLUTION: On Monday, Roger drove to work in 2 hours. On Tuesday, he averaged 15 miles per hour more, and it took him 30 minutes less to get to work. How far (in miles) does he travel to work

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: On Monday, Roger drove to work in 2 hours. On Tuesday, he averaged 15 miles per hour more, and it took him 30 minutes less to get to work. How far (in miles) does he travel to work      Log On


   

Question 201779: On Monday, Roger drove to work in 2 hours. On Tuesday, he averaged 15 miles per hour more, and it took him 30 minutes less to get to work. How far (in miles) does he travel to work?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A basic formula, which we need for this problem, is that distance = (average speed)*(time). d=rt for short.
If we let x = Roger's average speed on the first day, then his average speed on the second day would be (x+15), since we are told he drove 15 miles per hour faster. The time spent traveling on the first day is 2. The time spent traveling on the second day was 30 minutes (or 1/2 hour) less. (We will use 1/2 hour so that all our times are in hours.) 2 - (1/2) = 3/2 so he spent 3/2 hours traveling on the second day.
Using d=rt we can say:
  • the distance on the first day would be 2*x
  • On the second day the distance traveled would be (x+15)*(1/2).

But this distance traveled by Roger was the same on both days. This means that
2%2Ax+=+%28x%2B15%29%2A%283%2F2%29
Now we solve this using Algebra. First we will multiply out the right side using the Distributive Property:
2x+=+x%2A%283%2F2%29+%2B+15%2A%283%2F2%29
Simplifying
2x+=+%283%2F2%29x+%2B+45%2F2
Subtracting %283%2F2%29x from both sides we get
%281%2F2%29x+=+45%2F2
Now we divide both sides by 1%2F2 (or multiply both sides by the reciprocal of 1%2F2 (which is 2)). Either way we get
+x+=+45+
If we look back we will see that we decided that "x" was the speed on the first day. So we have found that Roger's average speed on the first day was 45 miles per hour.
But question asks for his distance. (Always remember to check to see if you have answered the question! It is very tempting, once you have "x = ...", to feel like you are finished.) Looking back we can see that his distance on the first day was 2x. (We could use (x+15)*(3/2), instead, but 2x is easier.) So the distance Roger traveled was 2*45 or 90 miles.