Respuesta :
Answer:
Boat speed 9.66 mph
Step-by-step explanation:
Boat speed x mph
current speed 4 mph
against current x- 4 mph
with current x+ 4 mph
Distance= 8 miles
Time against + time with =2 hours
t=d/r
8/(x+4) +8/(x-4)= 2
LCD =(x-4)(x+4)
8*(x-4) +8(x+4) =2(x^2-16)
8x-32+8x+32=2(x ^2-16)
16 x = 2 x ^2 -32
2 x ^2 - -16 x - 32 =0
divide by 2
x^2-8x-16=0
Find the roots of the equation by quadratic formula
a= 1 , b= -8 , c= -16
b^2-4ac= 64 + 64
b^2-4ac= 128
%09sqrt%28%09128%09%29=%0911.31%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 8 + 11.31 )/ 2
x1= 9.66
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 8 -11.31 ) / 2
x2= -1.66
Ignore negative value
Answer:
Boat's Rate: r = 5.63587
Step-by-step explanation:
Givens
- t = 10 hours
- r = rate of the boat
- r1 = 5 mph which is the rate of the steam.
- d = 6 km
Formula
- d = r * t
- transposed t = d/r
Formula
d/(r + 5) + d/(r - 5) = 10
Solution
- 6 (1 / (r + 5) + 1 / (r - 5) ) = 10 Divide by 6
- ( 1 / (r + 5) + 1 / (r - 5) ) = 10/6 = 1.6667 Multiply by the LCM on both sides
- LCM = ( r + 5) * (r - 5)
- ( r - 5 + r + 5) / ( (r + 5)(r - 5) = 1.6667 Combine the left side
- (2r )/( (r - 5)(r + 5) ) = 1.6667 Multiply by the LCM on both sides.
- 2r = 1.6667 * (r - 5)(r + 5) Divide by 2
- r = 0.833335 * (r - 5)(r + 5) Combine the right side
- r = 0.833335 (r^2 - 25) Remove the brackets
- r = 0.833335*r^2 - 20.833335 Subtract r from both sides
- 0 = 0.833335*r^2 - r - 20.833335
- Use the quadratic formula to solve this
- a = 0.833335
- b = -1
- c = -20.833335
- The value that comes out that matter is
- r = 5.63587
