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?
1 answer:
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 <em>x mi</em>, and that of Erin is given by <em>y mi</em>.
Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>
Which by cross-multiplying gives <em>distance = speed × time</em>.
Let time taken to cover the distance be <em>t h</em>.
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 <em>time t.</em>
(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.
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The missing figure is attached down
Answer:
Container A is filling more quickly
Step-by-step explanation:
<em>Let us explain the linear relation</em>
The linear equation is y = m x + b, where
- m is the slope of the line which represents the rate of change (change in y/change in x)
- b is the y-intercept which means the initial amount of y (at x = 0)
<em>If a line represents the amount of water over time, then it represents the rate of filling of the water</em>
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∵ The two lines represent the amount of water over time in
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