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.
