Reasoning · Grade 3-1 Speed and Distance
Problem
500 in two minutes is 250 a minute; the chaser does 300.
To compare two runners I need the same time unit; turning '500 in 2 minutes' into 'per minute' makes them comparable.
4.MD.A.2Analyze The UnitsGoing the same way, the gap closes 50 a minute.
When you chase someone in the same direction, only the extra speed you have over them eats into the gap.
4.NBT.B.4Draw A DiagramChasing someone in the same direction, only the extra speed you have over them eats into the gap.
Both runners move forward every minute, so the part of the speed they share moves the pair along without closing anything between them.
That leftover speed acts steadily, so twice the time closes twice as much of the gap and the closing scales with the minutes.
A 200 gap closes in 200 ÷ 50 = 4 minutes.
Number of minutes equals the gap shared out at 50 yards per minute; in 4 minutes Liam runs 1200 yd and Noah reaches 200 + 1000 = 1200 yd, so they meet.
4.OA.A.3Analyze The UnitsTwo more minutes of walking covers the remaining 180.
The meeting point splits the path; the part on Ava's side equals what Ava covered, and Mia walks that same part after the meeting.
4.MD.A.2Draw A DiagramThe other had walked that 180, so they met after 3 minutes.
Ava's part of the path, shared out at her speed, tells how long both had been walking when they met.
4.OA.A.3Guess And CheckTheir three minutes together span 270 + 180 = 450.
Walking toward each other, the two people together close the whole distance, so their combined travel until meeting is exactly A-to-B.
4.OA.A.3Analyze The UnitsMake every speed 'per minute' first, then chasing uses the speed difference and meeting uses the speeds added together!