Question

Greg and Erin start at the same point and begin running in different directions. Greg is running east at a speed of 7 miles per hour. Erin is running north at a speed of 9 miles per hour. After how many hours will they be exactly 15 miles apart?

Answer 1

Answer: The time at which the distance between the two is 150 miles is 1.3 hr.

Step-by-step explanation:

Step 1: Sketch the problem as shown in the attached image.

The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.

It follows the equation x² + y² = 15².

The distance covered by Greg is given by x mi, and that of Erin is given by y mi.

Step 2: To derive the distance covered by Erin and Greg, we use the formula Speed = distance ÷ time.

Which by cross-multiplying gives distance = speed × time.

Let time taken to cover the distance be t h.

Given that Speed of Erin is 9 mph and that of Greg is 7 mph.

Hence, distance covered by Greg, x = 7 × t = 7t.

Distance covered by Erin, y = 9 × t = 9t.

Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for time t.

(7t)² + (9t)² = 15²

49t² + 81t² = 225

(49 + 81)t² = 225

      t² = 225/(49 + 81)

      t² = 225/130

      t² = 1.730769231

       t = √1.730769231

       t = 1.315587029

t = 1.3hr

Hence the time at which the distance between the two is 150 miles is 1.3 hr.