Problem
Comparing speeds and distances
A car and a bike set off together and ride 5 minutes at steady speed. The car covers 1000 yards a minute, the bike 860. Find how much further the car goes in those 5 minutes.
Reasoning · Grade 3-1 Speed and Distance
Your answer
Watch out Subtracting 1 from 860 is meaningless — turn the kilometre into 1000 metres first.
How to solve
Strategy Analyze the Units — Both speeds are already in the same units (yards per minute), so I can compare them straight away. The shortest route is to find how much farther the car goes each minute, then add that head start over 5 minutes; I also break it into each total distance to double-check.
1STEP 1
Find the extra yards per minute
In matched units the car gains 1000 − 860 = 140 a minute.
1000 - 860 = 140 yd more each minute
Since both speeds use the same minute, just subtracting gives how much farther the car gets ahead in one minute.
4.NBT.B.4Analyze The Units2STEP 2
Multiply the extra by 5 minutes
Over 5 minutes that is 140 × 5 = 700.
140 × 5 = 700 yards
A steady gain each minute adds up by multiplying, so 5 equal gains of 140 make 700 yards.
4.MD.A.2Analyze The UnitsThe car gains 140 yards every minute, so over 5 minutes it gains five equal lots of 140.
Why?
Both vehicles cover ground every minute, so what actually opens the gap is only the amount by which one out-distances the other.
🧱A gap closes at the difference of the ratesWhen two things move the same way, neither speed alone matters — the gap between them shrinks at exactly the difference of the two speeds.
Why?
Five minutes each contributing the same 140 yards is five equal groups of 140, which is what multiplying counts.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
3STEP 3
Check by finding each total distance
Comparing 5000 with 4300 also leaves 700.
1000 × 5 = 5000, 860 × 5 = 4300, 5000 - 4300 = 700
Computing both whole trips and subtracting must match the per-minute method, which confirms 700 yards.
4.OA.A.3Identify SubproblemsAnswer
700 yards
140 × 5 = 700
700 yards is less than the car's full 5,000-yard trip and a bit more than half of one minute of the car's travel times five, which fits a 140-yard-per-minute lead over 5 minutes. Both methods agree, so the answer is solid.
Takeaway
Find the lead per minute, then multiply by the minutes - 140 yards ahead each minute over 5 minutes is 700 yards!
- Find the extra yards per minute
- Multiply the extra by 5 minutes
- Check by finding each total distance