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quester [9]
3 years ago
13

The cat is a high speed catamaran auto ferry that operates between city A and city B the cat can make the trip in about 2 and 1/

2 hours at a speed of 53 mph how far apart are city A and city B
Mathematics
1 answer:
Lyrx [107]3 years ago
4 0
If the CAT operates with a constant speed of 53 mph (which means it beats 53 miles in one hour) and makes a trip in about 2 and 1/2 hours, we just have to multiply 53 by 2 1/2 to find out the overall distance it's beating in that time:

53 * 2 1/2 =
= 53 * 2.5 =
= 132.5

Answer: City A is about <u>132.5 miles</u> from city B.
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Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
Natali [406]

Answers:

  • Total equation:  x+y = 80
  • Legs equation:  2x+4y = 248
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  • How many cows? 44

====================================================

Further explanation:

  • x = number of ducks
  • y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

  • 2x = number of legs from all the ducks only
  • 4y = number of legs from all the cows only
  • 2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

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