Depth · one concept from first principles · step 2 of 4
A taxi travels in one hour at a steady speed. A truck wants to cover the distance the taxi travels in hours minutes, but in hours at a steady speed. How many kilometers must the truck travel each hour?
An hour has 60 minutes, so 40 minutes is 40/60 = 2/3 of an hour.
The journey lasts 8/3 hours.
6.RP.A.2Analyze The UnitsMultiply the hourly distance by the number of hours, writing the mixed number as 402/5 first.
The taxi covers 1072/5 = 214.4 km.
7.RP.A.1Identify SubproblemsThe taxi covers in hours minutes.
At a steady speed every hour adds the same distance, so the distance over a stretch of time is that many hours of the one-hour distance.
hours minutes is hours because an hour is always the same minutes, so minutes can be renamed as two thirds of one.
The truck covers the same distance in 3 hours at a steady speed, so divide the distance by 3 to get one hour's worth.
The truck needs 1072/15 = 71 7/15 km each hour.
6.RP.A.3Work BackwardsA rate per hour only fits a time measured in hours -- change the units before you multiply.
A parent dashboard for the family lives at sensimlab.com.
The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Meeting Time with Piecewise Rates. Why the shapes repeat →