Question

A boat travels 6 km upstream and 6 km back. The time for the round trip is 10 hrs. The speed of the stream is 5 ​km/hr. What is the speed of the boat in still​ water? The speed of the boat is nothing ​km/hr.

Answer 1

Boat speed 9.66 mph

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 2

Boat's Rate: r = 5.63587

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