{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["total time","Sheet2","Sheet3"],"not_rendered":{"charts":3,"images":3,"macros":1,"defined_names":7,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"total time","index":0,"n_rows":43,"n_cols":18,"rows_kept":43,"merged":[[36,2,36,3]]}
[null,"  The Swim vs. Run Problem"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"       the calculus problem of finding"]
[null,null,"    the best combination"]
[null,null,"of running and swimming"]
[null,"    to get from one point A to another B"]
[null,null,"in the minimum time."]
[]
[]
["How fast can you run (10-20 ft/sec.)?",{"$nulls":4},{"$f":"D12","v":13}]
[{"$nulls":3},13,{"$f":"#REF!+D12*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
[]
["How fast can you swim (3 - 8 ft/sec.)?",{"$nulls":4},{"$f":"D16","v":6}]
[{"$nulls":3},6,{"$f":"#REF!+D16*(#REF!-#REF!)/100","v":{"$error":"#REF!"}}]
[]
[]
[]
[]
[{"$f":"\"Running \"&TEXT(1000-x0,\"0\") &\" feet at \" &TEXT(RR,\"0\") & \" feet per second takes \" &TEXT((1000-x0)/RR,\"0.0\") & \" seconds\"","v":"Running 768 feet at 13 feet per second takes 59.1 seconds"}]
[]
[{"$f":"\"Swimming \"&TEXT(Sheet2!L6,\"0\") &\" feet at \" &TEXT(s,\"0\") & \" feet per second takes \" &TEXT(Sheet2!L7,\"0.0\") & \" seconds\"","v":"Swimming 306 feet at 6 feet per second takes 51.1 seconds"}]
[]
[{"$nulls":3},"Total time =",null,{"$f":"(1000-x0)/RR +Sheet2!L7","v":{"v":110.12809566112747,"d":"110.1"}},"seconds"]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1",{"$nulls":9},"The graph of the function y =",null,null,{"$f":"\"(1000-x)/\" & TEXT(RR,\"0\") & \"+ sqrt(x^2 + 200^2)/\" & TEXT(s,\"0\")","v":"(1000-x)/13+ sqrt(x^2 + 200^2)/6"}]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[{"$nulls":11},"Select the point where you take to the water: x0 =",{"$nulls":4},{"$f":"O35","v":232},"feet"]
[]
[{"$nulls":14},232,{"$f":"Sheet2!H7+O35*(Sheet2!H8-Sheet2!H7)/100","v":2320}]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus",{"$nulls":8},"       The value of the derivative there is T' = ",{"$nulls":4},{"$f":"Sheet2!I25","v":{"v":0.0493119166770192,"d":"0.049"}}]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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