algebra problem

Question

Two boats leave port at the same time, one heading north at 35 knots, the other heading south at 47 knots.  How long will it take them to be 738 nautical miles apart (one knot = one nautical mile oer hour)

Answer 1

This is a basic D-I-R-T (Distance-Is-Rate-times-Time) problem.

We are given rate (speed) and total distance; we are asked to determine time.

 

The time for each boat is equal (T=D/R).  We write the equation realizing that the total distance is given:

          time of first boat   =    time of second boat

             T =   D / 35  =  (738 – D) / 47                  [now, we can solve for D]

             D/35 = (738-D)/47

            47D = 35(738-D)                        [cross-multiply]

            47D = 25830 – 35D                    [distribute]

           82D = 25830                               [add 35D to each side]

             D = 315

 

Remember that T=D/35:

       T = 315 / 35

      T = 9 hours

 

To check (very important):

  Is  9 = (738 – 315) / 47   ?

       9 =  423 / 47   ?

      9  =  9   ? yes