Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than 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 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?

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Question

12-06-2017
Mathematics

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Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than 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 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?

Please help ASAP

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metchelle metchelle · Answer 1 · 2017-06-25T05:34:04+02:00

Based on the problem above, given can be translated into the following terms,
Distance from A to 1st city = 100+x
Distance from 1st - 2nd city = x
Distance from 2nd - 3rd city = x-10
Total Distance = 100+x+x+x-10
D=90+3x (equation 1)
Since A to 1st city equal 2nd to 3rd city, D -2(x-10) = x
D-2x+20 = x (equation 2)
Solving two equations with two unknowns simultaneously,
x = -35/3,
substituting to equation 1, the total distance traveled is 55 miles