Problem
Unit distance is total distance divided by time
A taxi travels a fractional number of kilometers each hour. We need the hourly distance a truck must manage to cover the taxi's 2-hour-40-minute journey in 3 hours.
Ratios
Your answer
How to solve
Strategy Analyze the Units — Watch the units. An hourly rate can only multiply a time measured in hours, so change 40 minutes into a fraction of an hour first, find the distance, then divide it by the new time to get the new rate.
1STEP 1
Write the travel time in hours
An hour has 60 minutes, so 40 minutes is 40/60 = 2/3 of an hour.
2h 40min = 8/3 h
The journey lasts 8/3 hours.
6.RP.A.2Analyze The Units2STEP 2
Find how far the taxi goes
Multiply the hourly distance by the number of hours, writing the mixed number as 402/5 first.
402/5 × 8/3 = 1072/5
The taxi covers 1072/5 = 214.4 km.
7.RP.A.1Identify SubproblemsThe taxi covers in hours minutes.
Why?
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.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
hours minutes is hours because an hour is always the same minutes, so minutes can be renamed as two thirds of one.
🧱A bigger unit is a fixed count of smaller unitsA bigger unit always equals the same fixed number of smaller units (1 hour = 60 minutes, 1 km = 1000 m), so a measure can be renamed between them.
3STEP 3
Share that distance over three hours
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.
1072/5 ÷ 3 = 1072/15
The truck needs 1072/15 = 71 7/15 km each hour.
6.RP.A.3Work BackwardsAnswer
km
Multiply back: 1072/15 × 3 = 1072/5, the taxi's distance.
Takeaway
A rate per hour only fits a time measured in hours -- change the units before you multiply.
- Write the travel time in hours
- Find how far the taxi goes
- Share that distance over three hours