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Suppose you and 10 friends are taking a road trip for Spring Break. You plan on visiting multiple museums, national parks, and shopping locales along this trip. Your
road trip will a total of 10 days. You drive a total distance of 5000 miles. Some of the drive your average speed was 45 mph. While the rest of the trip was 70 mph.
1. How many hours were you driving each speed? Round 3 decimals
2. What distance did you drive for each speed? Round 3 decimals



Answer :

Using the relation between velocity, distance and time, and supposing the group travels for 8 hours a day, it is found that:

1. You were driving 24 hours at 45 mph and 56 hours at 70 mph.

2. You drove 1080 miles at 45 mph and 3920 miles at 70 mph.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

v = d/t.

For the first part, we have that:

  • The velocity is of 45 mph.
  • The distance is of d.
  • The time is of t.

Hence:

v = d/t

45 = d/t

d = 45t.

For the second part, we have that:

  • The velocity is of 70 mph.
  • The distance is of 5000 - d.
  • The time is of 80 - t. (10 days of 8 hours driving = 80 hours).

Hence:

70 = (5000 - d)/(80 - t).

d = 45t, hence:

70 = (5000 - 45t)/(240 - t).

5000 - 45t = 5600 - 70t

25t = 600.

t = 600/25

t = 24. -> (80 - 24) = 56.

d = 45t = 45 x 24 = 1080 -> (5000 - 1080) = 3920.

Hence:

1. You were driving 24 hours at 45 mph and 56 hours at 70 mph.

2. You drove 1080 miles at 45 mph and 3920 miles at 70 mph.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

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