Reasoning · Grade 6-1 Distance and Speed (2)
Problem
The current carries the boat 4 further an hour.
The current is a rate acting on everything floating, exactly like a moving walkway at an airport: standing still on it, you still get somewhere.
6.RP.A.2Draw A DiagramThe current carries everything floating on it, so in one hour it moves the boat its own distance whichever way the boat points.
What the boat achieves against the bank is its own speed and the current's taken together, so the two combine into one relative speed.
The current adds the same fixed distance every hour, so its effect can be written as a plain number of miles per hour.
Downstream the speed is 14.
Thinking about a single hour turns a confusing 'relative speed' into plain addition, and the answer being bigger than 10 is the check that you added in the right direction.
6.RP.A.3Solve An Easier Related ProblemDividing gives 5 hours.
Miles divided by miles-per-hour leaves hours. Because 14 x 5 = 70 exactly, this is a division you can confirm by multiplying straight back.
5.NBT.B.6Analyze The UnitsUpstream the speed is 6.
Same picture, arrows reversed: the current's 4 miles is subtracted rather than added, which is why upstream travel always looks painfully slow from the bank.
6.RP.A.3Draw A DiagramDividing gives 15 hours.
The same divide-distance-by-speed move as part (1); only the speed changed, which is the whole point of the problem.
5.NBT.B.6Analyze The UnitsMultiplying back confirms both.
Multiplying the speed by the time to rebuild the original distance is the standard check for any distance-speed-time answer, and the donated-versus-stolen tally shows the current's 4 miles per hour is doing exactly what the picture said.
4.MD.A.2Analyze The UnitsThe river moves the boat too: add the current when you go with it, subtract it when you go against it, and only then divide the distance by that speed.