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← All lessonsLesson 6 of 18 · 11 minutes

Yachtmaster School / Navigation

Get comfortable with navigation maths

Turn distance, speed and time into a useful estimate. No mental gymnastics needed.

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Our goal today

Calculate a simple passage time and recognise the limits of the estimate.

What you’ll practise

  • Keeping nautical miles, knots and hours consistent
  • Calculating separate legs and revised ETAs
  • Converting decimal hours and crossing midnight

Each question includes a custom diagram, the reasoning behind the answer, an explanation of the other choices and a follow-up exercise. Try the quiz first, or use the study view to read every answer.

01 / Learn

Keep the units together

For these exercises, use nautical miles for distance, knots for speed and hours for time. One knot is one nautical mile per hour. Distance = speed × time. Time = distance ÷ speed. Speed = distance ÷ time.

02 / Learn

Work an example slowly

Imagine a fictional 18-nautical-mile leg with a steady speed over the ground of 6 knots. The estimated time is 18 ÷ 6 = 3 hours. For a 9-mile leg at the same speed, 9 ÷ 6 = 1.5 hours: one hour and 30 minutes, not one hour and 50 minutes.

03 / Learn

Treat the answer as a planning estimate

Our examples assume a constant speed over the ground and no stops. Real trips involve changing conditions, manoeuvres and delays. Speed through the water is not automatically speed over the ground. Monitor your actual progress and revise your arrival estimate.

Your two-minute exercise

On paper, estimate a fictional 15-mile leg at 5 knots, then at 3 knots. Explain what changed and why the real arrival time could differ.

Keep learning from the source

Source check: . Scenarios and quiz questions are original YouSail practice material. Editorial policy.

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Have a go

Distance, Speed & Time Sailing Quiz

8 illustrated questions. Worked explanations and practical follow-ups for every answer.

At a constant 5 knots over the ground, how long does a 20-nautical-mile leg take?
A fictional passage of 20 nautical miles at 5 knots, with the travel time left unknown.
Estimate the timeIllustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 4 hours

Why this answer works

20 ÷ 5 = 4 hours. This calculation assumes a constant speed and no delays.

Why the other choices fall short

Two hours at 5 knots covers only 10 nm; five hours covers 25 nm. Checking each answer by multiplying speed by time is a useful way to catch a division error.

Put it into practice

Write units beside every value: 20 nm ÷ 5 nm per hour = 4 hours. For a real ETA, add the duration to departure time and allow for the plan's other constraints.

Check the lesson’s sources →Link to this question
What does 1.5 hours mean?
A clock face without hands beside a card labelled 1.5 hours, asking for hours and minutes.
Convert the timeIllustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 1 hour 30 minutes

Why this answer works

The decimal part is half an hour: 0.5 × 60 = 30 minutes.

Why the other choices fall short

The digit after the decimal is a fraction of an hour, not a number of minutes. Neither five minutes nor fifty minutes is half of a sixty-minute hour.

Put it into practice

Convert the fractional part separately: 0.5 × 60 = 30. Check that one hour plus thirty minutes converts back to 1.5 hours.

Check the lesson’s sources →Link to this question
At a constant 6 knots over the ground for 2.5 hours, how far do you travel?
A yacht travelling at 6 knots for 2.5 hours, with the passage distance left unknown.
Estimate the distanceIllustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 15 nautical miles

Why this answer works

Distance = speed × time, so 6 × 2.5 = 15 nautical miles.

Why the other choices fall short

Adding 6 and 2.5 produces 8.5 but does not calculate a distance. Twelve nautical miles accounts for only two hours and omits the remaining half-hour.

Put it into practice

Split the time: 6 × 2 = 12 nm, then 6 × 0.5 = 3 nm. Adding the two distances gives 15 nm and provides a quick check on the direct multiplication.

Check the lesson’s sources →Link to this question
Your actual speed over the ground drops. What should you do with the original arrival estimate?
Two progress lines comparing the original plan with a slower yacht; arrival time is unknown.
When progress changesIllustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: Revise it using the changed progress and conditions

Why this answer works

An estimate is only as useful as its assumptions. Recalculate when your actual progress changes.

Why the other choices fall short

Correct arithmetic cannot preserve an estimate after its input changes. Through-water speed alone omits the current's effect on progress over the ground.

Put it into practice

Measure or estimate remaining distance and sustained ground speed, then calculate remaining time. Record the time of the update so the new ETA has a clear basis.

Check the lesson’s sources →Link to this question
You leave at 09:20 for a fictional 18 nm leg at a constant 4.5 knots over the ground. With no stops, what is your estimated arrival time?
A yacht on an 18 nautical mile leg at 4.5 knots, departing at 09:20 with arrival time unknown.
Departure 09:20Illustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 13:20

Why this answer works

Time = 18 ÷ 4.5 = 4 hours. Add four hours to 09:20 to get 13:20. Keep decimal hours separate from clock time; real delays would require a new estimate.

Why the other choices fall short

Four hours added to 09:20 keeps the minutes at :20. The other clock times do not correspond to the calculated four-hour duration; do not treat 4.5 knots as four hours thirty minutes.

Put it into practice

Reverse-check 13:20 minus 09:20 = 4 hours, then 4 × 4.5 = 18 nm. This checks both the passage calculation and the clock addition.

Check the lesson’s sources →Link to this question
A fictional trip has two legs: 12 nm at 6 knots, then 9 nm at 3 knots, both speeds over the ground. How long does the whole trip take without stops?
Two consecutive passage legs labelled 12 nautical miles at 6 knots and 9 nautical miles at 3 knots; total time is unknown.
Two legs, one arrival estimateIllustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 5 hours

Why this answer works

Calculate each leg separately: 12 ÷ 6 = 2 hours and 9 ÷ 3 = 3 hours. Total: 5 hours. Averaging the two speeds without weighting for time gives the wrong answer.

Why the other choices fall short

Three and a half hours assumes 6 knots for the whole route; seven hours assumes 3 knots throughout. Four hours forty minutes comes from an unweighted 4.5-knot average, which ignores how long each speed applies.

Put it into practice

Make a row for each leg with distance, ground speed and duration. Add the durations only after calculating each leg, then add stops separately if the scenario includes them.

Check the lesson’s sources →Link to this question
At 14:10 you have 7.5 nm remaining. Your sustained speed over the ground is now 3 knots. What revised arrival time follows from that assumption?
Remaining passage of 7.5 nautical miles at 3 knots, with an update time of 14:10 and an unknown revised arrival.
Update at 14:10Illustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 16:40

Why this answer works

7.5 ÷ 3 = 2.5 hours, which is 2 hours 30 minutes. Add that to 14:10 to get 16:40. Recheck the estimate if the sustained speed changes again.

Why the other choices fall short

16:10 allows only two hours and misses the half-hour; 17:10 allows three hours. A clock does not have a :60 minute value: carrying sixty minutes changes the hour.

Put it into practice

Convert 2.5 hours to 150 minutes before adding it to 14:10. Compare the revised ETA with any daylight, tide or crew constraints in the passage plan.

Check the lesson’s sources →Link to this question
A fictional 13.5 nm leg starts at 23:15. With a constant 4.5 knots over the ground and no stops, when is arrival?
A 13.5 nautical mile passage at 4.5 knots starts at 23:15 and asks for the arrival date and time.
Departure 23:15Illustrative · not to scale · tap to enlarge ↗
Read the answer and explanation

Answer: 02:15 the next day

Why this answer works

Duration = 13.5 ÷ 4.5 = 3 hours. There are 45 minutes until midnight and another 2 hours 15 minutes afterwards, so arrival is 02:15 on the next date. The date change is part of a clear ETA.

Why the other choices fall short

01:45 allows only 2.5 hours; 03:15 allows four. Writing 02:15 on the departure date places the arrival before the 23:15 departure rather than three hours after it.

Put it into practice

Write departure date and time as well as the duration. On an overnight plan, keep the date and time convention explicit when comparing forecasts and tidal information.

Check the lesson’s sources →Link to this question

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Practice only: this quiz is not an official RYA examination or an assessment of practical competence. Leaving mid-quiz starts that attempt again.

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