Reasoning · Grade 6-1 Distance and Speed (1)
Problem
With mixed units nothing can be compared.
Checking the units before doing any arithmetic is the habit that saves this whole question. A rate is a pair - a distance and a time - and two pairs can only be ranked when both halves are in matching units.
6.RP.A.2Analyze The UnitsTake the common unit as metres per minute.
A unit rate is a rate rewritten so the bottom number is 1. Once every speed says 'per 1 minute', the top numbers can be compared directly, which is exactly what makes unit rates worth the trouble.
6.RP.A.2Organize Information In More WaysChoosing metres per minute as a common unit is what makes three speeds comparable at all.
A bigger unit is always the same fixed count of smaller ones, so any speed can be renamed into metres per minute without changing it.
Once all three are numbers in the same unit, comparing them two at a time chains into one full ordering.
The first works out to 80.
Scaling both halves of a rate by the same number keeps the pace the same - it is the same walk, just watched for ten times as long. Choosing 10 because 6 x 10 = 60 avoids any division at all.
6.RP.A.3Solve An Easier Related ProblemThe second works out to 75.
Doing the conversion in two small steps - down to one hour, then down to one minute - keeps the divisors at 2 and 60 instead of one awkward 120, and each step is a sentence you can say out loud.
4.MD.A.1Analyze The UnitsThe third works out to 76.
Her distance was already in metres and her time already in minutes, so the only work left was making the time equal 1 - a reminder that not every line of a problem costs the same effort.
6.RP.A.3Solve An Easier Related ProblemNow they order as 80, 76, 75.
Writing all three converted rates in one short list, rather than comparing them two at a time from memory, is what keeps a near-tie like 76 against 75 from being read the wrong way round.
6.RP.A.3Make A Systematic ListIn order that is Mia, Nora, Jonah.
The question asks for names, not numbers, so the last step is simply reading the ranking back out as words.
6.RP.A.2Make A Systematic ListYou can't tell who is faster until every speed says the same thing - so turn them all into 'metres in one minute' first, then just read off the biggest.