Question

You are kayaking along a 24-mile stretch of river. You travel 6 miles per hour when paddling and 2 miles per hour when drifting. Give three possible combinations of paddling and drifting times. Write your answers as ordered pairs.

Answer 1

(1,6), (2,6), (3,3)

Explanation:

Since you travel 6 miles per hour when paddling and 2 miles per hour when drifting, and the total distance covered is 24 miles, we find the times t and t' of paddling and drifting respectively in which the product 6t + 2t' = 24.

So, for the first values of t and t' , we have t = 1 and t' = 9

So, 6t + 2t' = 6 × 1 + 2 × 9 = 6 + 18 = 24

As an ordered pair (1, 9)

For the second set of values of t and t' , we have t = 2 and t' = 6

So, 6t + 2t' = 6 × 2 + 2 × 6 = 12 + 12 = 24

As an ordered pair (2, 6)

For the third set of values of t and t' , we have t = 3 and t' = 3

So, 6t + 2t' = 6 × 3 + 2 × 3 = 18 + 6 = 24

As an ordered pair (3, 3)

So, the three different combinations of paddling and drifting times are (1,6), (2,6), and (3,3)