Answer: the rate of the river's current is 14 mph.
Step-by-step explanation:
Let x represent the rate of the river's current.
The speed of the motor boat in still water is 35 mph.
Since the boat travelled more miles downstream than upstream at the same time, it means that while going downstream, it moved in the direction of the current and while going upstream, it moved against the direction of the current. The total speed downstream would be
(35 + x) mph and the total speed upstream would be (35 - x) mph.
Time = distance/speed
If the boat can travel 7 miles downstream, the time spent travelling downstream is
7/(35 + x)
At the same time it takes to travel 3 miles upstream, the time spent travelling upstream is
3/(35 - x)
Since the time is the same, then
7/(35 + x) = 3/(35 - x)
Cross multiplying, it becomes
7(35 - x) = 3(35 + x)
245 - 7x = 105 + 3x
3x + 7x = 245 - 105
10x = 140
x = 140/10
x = 14
Hello from MrBillDoesMath!
Answer:
x = 1/2 (1 +\- i sqrt(23))
Discussion:
x \3x - 2 = (x/3)*x - 2 = (x^2)/3 - 2 (*)
1 \3x - 4 = (1/3)x - 4 (**)
(*) = (**) =>
(x^2)/3 -2 = (1/3)x - 4 => multiply both sides by 3
x^2 - 6 = x - 12 => subtract x from both sides
x^2 -x -6 = -12 => add 12 to both sides
x^2-x +6 = 0
Using the quadratic formula gives:
x = 1/2 (1 +\- i sqrt(23))
Thank you,
MrB
Answer:
Monthly payment is $5970
Step-by-step explanation:
Given : April invested in a lifetime annuity that begins payments at age 65. Her life expectancy is 89. April invested a $1,000,000 into the annuity, which earns 4.4% APR compounded monthly.
To find : what is April's monthly payment amount?
Solution :
Formula of monthly payment
Monthly payment, 
Discount factor 
Where, Amount = $1,000,000
Rate r= 4.4%=0.044 compounded monthly
Time = 89-65=23 years
Now, put all the values we get,
Monthly payment,
Approximately,monthly payment is $5970
