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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Answer:
7,200
Step-by-step explanation:
Let's start by calculating how many students the university accepts. The problem says they accept 60% of the students. 60% as a decimal is 0.6. To calculate 60% of something, you multiply .60 by whatever quantity. In this case, it would be the students.
Number of accepted students = = 18,000
The university accepts 18,000 students.
Now, the next problem is that of those accepted students, we need to find out how many actually enroll. The problem says they accept 40% of the accepted students. Applying the same principle,
Number of enrolled students = = 7,200
The number of students that actually enroll is 7,200.
Alternatively, would give you the same result.
Combining the pieces together, we are asking for 60% of 30,000. Then getting 40% of that 60%.