Answer: 46 years
Step-by-step explanation:
Let the father's age be x and the son's age be y, then 3 years ago:
Father = x - 3
son = y - 3
Then , from the first statement :
x - 3 = 3 ( y - 3 )
x - 3 = 3y - 9
x = 3y - 9 + 3
x = 3y - 6 .......................................... equation 1
In five years time
father = x + 5
son = y + 5
Then , from the second statement
x + 5 = 2 ( y + 5 )
x + 5 = 2y + 10
x = 2y + 10 - 5
x = 2y + 5 ........................ equation 2
Equating equation 1 and 2 , we have
3y -6 = 2y + 5
add 6 to both sides
3y = 2y + 5 + 6
subtract 2y from both sides
3y - 2y = 11
y = 11
substitute y = 11 into equation 1 to find the value of x
x = 3y - 6
x = 3(11) - 6
x = 33 - 6
x = 27
This means that the father is presently 27 years and the son is presently 11 years.
In four years time
father = 27 + 4 = 31
son = 11 + 4 = 15
sum of their ages in four years time will be
31 + 15 = 46 years
I think it is C
Hope this helped
7(x + 2) = 6(x + 5)
7x + 14 = 6x + 30
x + 14 = 30
x = 16
Answer:
B
Step-by-step explanation:
Answer:
285,753 cm³/min
Step-by-step explanation:
The rate of change of volume is the product of the water's surface area and its rate of change of depth.
At a depth of 2 m, the water has filled 1/3 of the 6 m depth of the tank. So, the radius at the water's surface will be 1/3 of the tank's radius of 2 m. The water's surface area is ...
A = πr² = π(2/3 m)² = 4π/9 m²
The rate of change of depth is 0.2 m/min, so the volume of water is increasing at the rate ...
dV/dt = (0.20 m/min)(4π/9 m²) = 8π/90 m³/min ≈ 279253 cm³/min
This change in volume is the difference between the rate at which water is being pumped in and the rate at which it is leaking out:
2.8×10⁵ cm³/min = (input rate) - 6500 cm³/min
Adding 6500 cm³/min to the equation, we get ...
input rate ≈ 285,753 cm³/min
