Let the speed of river be x km/hr down stream.
Time = Distance / speed
Since river flows downstream, speed of boat down stream = Speed of boat + speed of river = (15 + x).
Since river flows downstream, speed of boat upstream = Speed of boat - speed of river = (15 - x).
Time Upstream - Time Downstream = 75 minutes
Time Upstream = 45 / (15 - x)
Time Downstream = 45 / (15 + x)
75 minutes = 75/60 = 5/4 hours
Time Upstream - Time Downstream = 75 minutes = 5/4 hours
45 / (15 - x) - 45 / (15 + x) = 5/4 Divide both sides by 45
1 / (15 - x) - 1 / (15 + x) = (5/4)*(1/45)
1 / (15 - x) - 1 / (15 + x) = 1/36
((15 + x) - (15 -x)) / (15-x)(15+x) = 1/36
(15 +x - 15 +x) / (15-x)(15+x) = 1/36
2x / (15-x)(15+x) = 1/36
(15-x)(15+x) = 2x*36
(15-x)(15+x) = 72x
225 - x² = 72x
0 = x² + 72x -225
x² + 72x -225 = 0 This is a
quadratic function, use a calculator that can solve the function, by
inputting the function.
x = 3, or -75. Since we are solving for speed, we can not have negative values.
x = 3 is the only valid solution.
Speed of the river = 3 km/hr downstream.
Copyright.
This can be treated as a proportion problem.
Larger solid:
Surface area = 1,372 cm²
Volume = 1,801 cm³
Smaller solid:
Surface area = 1,008cm²
Volume = ?
1,372 / 1,801 = 1008 / x
1,372 * x = 1,801 * 1008
1,372x = 1,815,408
x = 1,815,408 / 1,372
x = 1,323.18
The volume of the smaller solid is 1,323.18 cm³
Answer:
15
Step-by-step explanation:
Let n, d, q represent the numbers of nickels, dimes, and quarters. The problem statement tells us ...
n +d +q = 37
n = d +4
q = n +2
___
Rearranging the second equation gives ...
d = n -4
Substituting that into the first, we get ...
n + (n -4) +q = 37
2n +q = 41 . . . . . . . add 4 and simplify
Rearranging the third original equation gives ...
n = q -2
Substituting into the equation we just made, we get ...
2(q -2) +q = 41
3q = 45 . . . . . . . . add 4 and simplify
q = 15 . . . . . . . . . divide by 3
Joe has 15 quarters.
_____
<em>Check</em>
The number of nickels is 2 fewer, so is 13. The number of dimes is 4 fewer than that, so is 9. The total number of coins is 15 + 13 + 9 = 37, as required.
A.) 1
Type it in your calc. to find
Answer:
- Annie- 17 hours, Brian- 3 hours
Step-by-step explanation:
Let the number of hours Annie travelled be a, and same of Brian be b
<u>Then we have</u>
<u>Substituting a in the first equation</u>
- 5b + 2 + b = 20
- 6b = 20 - 2
- 6b = 18
- b = 3
<u>Then finding a</u>
<u>So the answer is:</u>
- Annie- 17 hours, Brian- 3 hours
