Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than 1/3 the distance from the first city to the second city. The distance from the second city to the third city was 10 miles less than 5/4 the distance from the first city to the second city. If the distance from his original location to the first city and the distance from the second city to the third city were the same, what was the total distance Eric traveled?
+150 Well think about it, the key words there are more than and less than so if he traveled let's say from his house until the first city that's 100 miles for the first one and then they say that he traveled 10 miles less than the distance from the first city until the second city. The total distance is 280 because if you read the very last sentence it says that from the original distance from the first city is about 100 miles and then it says if the the distance from the second city to the third city was the same that means that the equation goes like this: (90*2)+100 and in order to get this correctly you must do P.E.M.D.A.S which is parenthesis, exponents, multiplying, dividing, adding and subtracting so there you go.
Let the distance between the origin and the 1st city =D =The distance between 2nd and 3rd city.
Let the distance between 1st and 2nd city = d,then:
The distance between origin and 1st city =1/3d + 100, and
The distance between 2nd and 3rd city =5/4d - 10. But we have:
1/3d + 100 = D..........(1), and
5/4d - 10 = D.............(2), but
1/3d + 100 = 5/4d - 10, solve for d
d = 120 miles - distance between 1st and 2nd city.
1/3 x 120 + 100 = 140 miles - distance between origin and 1st city.
5/4 x 120 - 10 = 140 miles - distance between 2nd and 3rd city.
140 + 120 + 140 = 400 miles - total distance travelled.
