Question

Exits on an interstate are numbered consecutively. The distance between Exit 12 and Exit 13 is 2.7 miles. The distance between Exit 13 and Exit 14 is 0.9 mile farther than the distance between Exit 12 and Exit 13. The distance between Exit 13 and Exit 15 is 6.8 miles farther than the distance between Exit 12 and Exit 14. The distance between Exit 14 and Exit 15 is miles.

Answer 1

The distance between Exit 14 and Exit 15 is 9.5 miles

Step-by-step explanation:

Exits on an interstate are numbered consecutively

The given is:

1. The distance between Exit 12 and Exit 13 is 2.7 miles

2. The distance between Exit 13 and Exit 14 is 0.9 mile farther than the

    distance between Exit 12 and Exit 13

3.The distance between Exit 13 and Exit 15 is 6.8 miles farther than the

   distance between Exit 12 and Exit 14

We need to find the distance between Exit 14 and Exit 15

∵ The distance between Exit 12 and Exit 13 is 2.7 miles

∵ The distance between Exit 13 and Exit 14 is 0.9 mile farther than the

   distance between Exit 12 and Exit 13

∴ The distance between Exit 13 and Exit 14 = 2.7 + 0.9 = 3.6 miles

Assume that the distance between Exit 14 and Exit 15 is x

∵ The distance between Exit 12 and Exit 14 = 2.7 + 3.6 = 6.3 miles

∵ The distance between Exit 13 and Exit 15 = 3.6 + x miles

∵ The distance between Exit 13 and Exit 15 is 6.8 miles farther than the

   distance between Exit 12 and Exit 14

∴ 3.6 + x = 6.3 + 6.8

∴ 3.6 + x = 13.1

- Subtract 3.6 from both sides

∴ x = 9.5 miles

The distance between Exit 14 and Exit 15 is 9.5 miles

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