How far away is Neptune's moon, Triton, from earth and how long would it take to get there?

Approximately 2.7 billion miles. It would take the fastest spacecraft approximately 8 years and 9 months, or 3,193 days.

2.7 billion miles is about 4.34 billion kilometers. The fastest spacecraft ever built is New Horizons, which travels at about 15.73 kilometers per second.

4,340,000,000km##/##15.73 ##(km)/s## = 275,905,912 seconds

275,905,912 s / ##(60s)/(1min)##= 4,598,431 minutes

4,598,431 m / ##(60m)/(1hr)##=76,640 hours

76,764 hr / ##(24hr)/(1day)##=3193 days

3193 days / ##(365days)/(1year)## = 8.74 years, or about 8 years and 9 months.