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One triangle, three questions

How Long Will the Journey Take?

Speed, distance and time are the same fact asked three ways.

Sixty miles an hourDistance, speed and timein one triangle
The unit tells you the sum: miles per hour is miles ÷ hours.

  1. Step 1 of 5

    Speed is a division already.

    1 120 miles2÷÷ 2 hours3 60 miles perhour

    Miles per hour means miles divided by hours. The word 'per' is a division sign that has been spelled out.

  2. Step 2 of 5

    So the other two questions rearrange it.

    Distance×Speed × timeTime÷Distance ÷ speed

    Distance is speed times time. Time is distance divided by speed. Three questions, one relationship, no new maths.

  3. Step 3 of 5

    The units have to match.

    Matching units 60 mph for 0.5 hours =30 milesMismatched?60 mph for 30 minutes =1,800?

    Miles per hour with minutes gives nonsense. Converting the minutes to hours first is where most wrong answers come from.

  4. Step 4 of 5

    Average speed is not the average of speeds.

    Guessed averagethe middle ofthe speedsActual averageweighted by timespent

    Half the journey at 30 and half at 60 does not average 45, because you spend twice as long on the slow half.

  5. Step 5 of 5

    Which is why speeding saves so little.

    At 30 mph20 minutesAt 40 mph15 minutes

    On a ten-mile trip, driving ten miles an hour faster saves a couple of minutes. The distance is short and the sum is unforgiving.

    Pilots and sailors use the same triangle, and so does anyone working out when to leave for a train.

The short version

Speed, distance and time are one relationship rearranged three ways, and the units must match before any of it works.

Try it yourself

Time a walk and measure the distance. Divide to get your speed, then predict a longer walk and check it.

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