cant figure out how to solve the 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 per hour)

Answer 1

So we have two funds so the money is split: 18750 = x + y

where x is the amount put into the first fund, and y is the amount put into the second fund.

We are also given that the total interest is  $2117.

the formula for annual interest is P = P₀(1+r)^t where

P is the current amount, P₀ is the initial amount, t is the time in years, and r is the decimal equivalent for interest.

Thus we have for fund 1

P₁ = x(1+.12)¹ = 1.12x 

and 

P₂ = y(1+.10)¹ = 1.1y  

 

We have that P₁ + P₂ = P₀ + Interest = 18750 + 2117.

(total amount = principal + interest)

So substitute and get

1.12x + 1.1y = 20867

 

Now we solve the system of equations

      x +      y = 18750

1.12x + 1.1y = 20867

 

multiply equation 1 by -1.1 to cancel out the y to get

.02x = 242

so x = 12100 and thus y is 6650