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Amiraneli [1.4K]
2 years ago
8

You and two friends plan to walk your dogs together. You want the meeting place to be the same distance from each person’s resid

ence. Explain how you can use the diagram to locate the meeting place.

Mathematics
1 answer:
AveGali [126]2 years ago
6 0
If we join the points we are gonna end up with a triangle, from there by finding the centroid of the triangle we will get a point which is equidistant from all the three points given in the diagram.

Formula for Centroid:
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Adam started to run at a rate of 6 mph from city A towards city B, which is 18 miles away. Ten minutes later, Benjamin started t
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Answer:

<u>Benjamin's rate in mph was 6.44</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

  • Rate or speed of Adam = 6 mph
  • Ten minutes later, Benjamin started to run from city B towards city A
  • Simultaneously, Caroline started to bicycle at a rate of 11 mph from city A towards city B

2. If Caroline caught up to Benjamin 50 minutes after passing Adam, what was Benjamin's rate in mph?

A. Let's calculate when Caroline caught up Adam:

Adam's rate = 6 mph

Caroline's rate = 11 mph

10 minutes = 1/6 of an hour

Distance covered by Adam when Caroline started to bike = 6 * 1/6 = 1 mile

t = Time it took Caroline to catch up to Adam

Therefore, we can solve for t, this way:

11t = 6t + 1

11t - 6t = 1

5t = 1

t = 1/5 of an hour

t = 12 minutes

Caroline passed Adam after biking 12 minutes, therefore she caught up to Benjamin 50 minutes later, or after 62 minutes.

B. Let's calculate the distance she covered after 62 minutes, this way:

62 minutes = 1 hour and 2 minutes or 1 2/60 or 1.03

Distance covered by Caroline = Time * rate

Replacing with the values we have:

Distance covered by Caroline = 1 2/60 * 11

Distance covered by Caroline = 11 11/30 or 11.37 miles

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C. Finally let's calculate Benjamin's rate, this way:

Rate = Distance/Time

Replacing with the values we know:

Rate = 6.63/1.03

<u>Rate = 6.44 mph (rounding to the next hundredth)</u>

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Answer:

(0, 2)

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