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ioda
2 years ago
9

Paulina swims 5 miles down a creek with a current for 2 hours. It takes her 4

Mathematics
1 answer:
Westkost [7]2 years ago
4 0

Answer: her swimming speed = 1.875 mph

Speed of current = 0.625 mph

Step-by-step explanation:

Let x represent her swimming speed.

Let y represent the speed of the current.

Paulina swims 5 miles down a creek with a current for 2 hours. Since this is faster, it means that she swam with the current. Her total speed would be (x + y) mph

Distance = speed × time

Therefore,

5 = 2(x + y)

dividing both sides by 2, it becomes

2.5 = x + y- - - - - - -1

It takes her 4 hours to swim the same 5 miles back to her original destination against the

same current. It means that her total speed was (x - y) mph

Distance covered would be

5 = 4(x - y)

Dividing both sides by 4, it becomes

1.25 = x - y- - - - - - - 2

Adding equation 1 to equation 2, it becomes

3.75 = 2x

x = 3.75/2

x = 1.875

Substituting x = 1.875 into equation 1, it becomes

2.5 = 1.875 + y

y = 2.5 - 1.875

y = 0.625

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A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk
Tcecarenko [31]

Answer:

  • T(x) = (√(4+x^2))/2 +(c -x)/4
  • (a) x = 1.155 miles
  • (b) x = 1/2 mile

Step-by-step explanation:

The straight line distance from the starting point to the point x on the road is given by the Pythagorean theorem:

  d1 = √(2²+x²)

The time required to walk that distance in the woods (at 2 miles per hour) is ...

  time = distance / speed

  t1 = √(4+x²)/2

The remaining distance along the road to the car is ...

  d2 = c - x . . . . . for c > x

and the corresponding time at 4 mph is ...

  t2 = (c -x)/4

Then the total time is ...

  T(x) = t1 +t2

  T(x) = √(4+x²)/2 +(c -x)/4

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(a) The value of x that minimizes total time is the one that makes the derivative zero.

  T'(x) = x/(2√(4+x²)) -1/4

  0 = (2x -√(4+x²))/(4√(4+x²))

  √(4+x²) = 2x . . . . . fraction is zero when numerator is zero; add radical

  4 +x² = 4x² . . . . . . square both sides

  4/3 = x² . . . . . . . . . subtract x², divide by 3

  x = (2/3)√3 ≈ 1.1547

If c = 9 miles, x = 1.1547 miles.

__

(b) For c < (2/3)√3, the shortest travel time will be along the straight-line path to the car.

If c = 1/2 mile, x = 1/2 mile.

8 0
2 years ago
Solve the equation or inequality 3/2t-16=4/3t-6
Tamiku [17]

Answer:

<em>t=60</em>

Step-by-step explanation:

3/2t-16=4/3t-6

(subtract 4/3t from both sides)

3/2t-16-4/3t=-6

(add 16 to both sides)

3/2t-4/3t=-6+16

(simplify)

1/6t=10

(divide by 1/6 (or multiply by 6 on both sides)

t=60

7 0
2 years ago
The bird house in your friend's yard casts a shadow that is 14 feet long. Your friend is 5 feet tall and casts a shadow that is
astra-53 [7]
3.5/5=14/x   20ft tall
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2 years ago
You’re assembling desserts with a friend. Together you can make 12 desserts in five minutes. Two more friends arrive and you are
Dafna1 [17]
Well there's 10 minutes in the second part so first 48/2 is 24. Now 24/4 (since there's 4 people so far) is 6, now 6*6 because there's now 6 people in total so the final answer is 36 in 5 minutes
8 0
2 years ago
The table below shows the typical hours worked by employees at a company. A salaried employee makes $78,000 per year. Hourly emp
MrRa [10]

Given:

  • The table of typical hours worked by employees at a company
  • salaried employee makes $78,000 per year
  • hourly employees get $26 per hour and $39 per hour when they work more than 40 hours.

To Find: Which payment option to recommend to a new employee.

Solution: I would recommend being a salaried employee.

Explanation:

We begin by calculating the typical number of hours worked per week.

Adding up the hours from the table, we have 0+8+8.5+9.5+10+8+3=47.

The payment for an hourly employee must be calculated as $26 per hour for working till 40 hours, and $39 per hour when they work more than 40 hours.

So, the payment for 47 hours of work per week will be (26)(40) + (39)(7) = 1313 dollars.

As there are 52 weeks in a year, the yearly payment for an hourly emplyee would be (1313)(52) = 68276. That is, an hourly employee would earn $68276.

On the other hand, we are given that a salaried employee makes $78000 per year which is more money than what an hourly employee makes for the same amount of work.

Therefore, I would recommend a new emplyee to be paid a salary rather than work on an hourly basis.


6 0
2 years ago
Read 2 more answers
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