Duncan picks a number and will subtract

6

each second. George picks a different number and will add

8

each second. They begin at the same time, and after

14

seconds, they both arrive at the number

25

. What is the sum of Duncan's and George's starting numbers?

To answer, let's set up a system of equations:

For Duncan:

-6 (14) + b = 25, where b is his starting number

For George:

8 (14) + c = 25, where c is his starting number

Solving for b:

-6 (14) + b = 25

-84 + b = 25 Add 84 to both sides

b = 109

Solving for c

8 (14) + c = 25

112 + c = 25 Subtract 112 from both sides

c = - 87

Duncan's number was 109, and George's number was - 87

Their sum is:

109 + (-87) = 22

Answer is 22