Reasoning · Grade 2-2 Time and Duration
Problem
Train 1 gives 30 min for the first leg and 50 min for the second.
When both endpoint times are known, the elapsed time between them is just the difference.
3.MD.A.1Identify SubproblemsTrain 2 shows the last leg as 80 min, which Train 1 shares.
Same speed means the last segment takes the same 80 minutes for both trains, so Train 2's known values hand us Train 1's missing piece.
3.MD.A.1Look For A PatternTrain 1 takes 170 min from Midtown to Harborport, so taking off 80 leaves 90 min.
A whole trip is the sum of its parts, so subtracting the known part leaves the unknown part.
3.MD.A.1Identify SubproblemsTaking the known segment times away from the whole journey leaves exactly the missing Midtown-to-Lakeview segment.
The stations cut the journey into segments that follow one after another with no gap and no overlap, so the segments add back to the whole trip.
With the whole and all but one part in hand, subtracting hands back the one part that was missing.
So Train 1 reaches Lakeview at 8:20 + 90 min = 9:50.
Adding the segment time to the earlier station's time gives the next arrival, and it lands exactly on the known final time.
3.MD.A.1Identify SubproblemsBacking 30 min off Train 2's 10:35 puts Riverside at 10:05.
Knowing the later station and the segment time lets us step backward to the earlier station.
3.MD.A.1Work BackwardsTrain 2's Midtown is 10:35 + 50 min = 11:25.
Adding the Greenfield-to-Midtown segment gives Midtown, and the later given times confirm it is right.
3.MD.A.1Identify SubproblemsSame speed means each leg takes the same minutes for both trains, so a time known on one train fills the gap on the other. Just Grade 3 elapsed-time adding and subtracting!