Finding the speed

Question

A boat swimmed 12 kilometres downstream and 12 upstream.The amount of time it swimmed is 1 hour and 40 minutes.Find the speed of the current if the boat's speed in a standing water is 15 km/h.

Answer 1

You can't fool me!

 

Boats don't swim!

Answer 2

d=rt

12=(r+c)t

12=(15+c)t

12=(15-c)(5/3-t)  where 1 hour 40 minutes=1 2/3 hours=5/3 hours

12/(15+c)=t

substitute

12=(15-c)(5/3-[12/(15+c)])

simplify(5/3-[12/(15+c)])

{5(15+c)-3(12)}/3(15+c)

(75+5c-36)/3(15+c)

(39+5c)/3(15+c)

12=(15-c)(39+5c)/3(15+c)

12(3)(15+c)=(15-c)(39+5c)

36(15+c)=(15-c)(39+5c)

540+36c=585-39c+75c-5c²

540+36c=585+36c-5c²

5c²-36c-585+540+36c=0

5c²-45=0

5c²=45

c²=9

c=±3

c=3 km/hr is the speed of the current

12=(15+3)(2/3)

12=18(2/3)

12=12

12=(15-3)(1)

12=12(1)

12=12

 

 

 

 

 

 

Answer 3

Hi Lody, this problem is an application of the D(istance) = R(ate) * T(ime) equation. We need to solve the equation for time. Let x be the speed of the current.

 

Equation downstream:

 

D_d = R_d * T_d

 

Solving for time:

 

T_d = D_d / R_d 

 

T_d =12 / (15 + x)

 

Equation upstream:

D_u = R_u * T_u

Solving for time:

T_u = D_u / R_u 

T_u =12 / (15 - x)

 

Solve:

 

We know the total time of the round trip is 1 hour and 40 minutes, or 1.67 hours.

 

That means:

 

T_d + T_u = 1.67

 

Substituting for T_d and T_u gives:

 

12 / (15 + x) + 12 / (15 - x) = 1.67

 

Find common denominator on the left side:

 

The common denominator is (15 + x) * (15 - x)

 

(12 * (15 - x) + 12 * (15 + x)) / ((15 + x) * (15 - x)) = 1.67

 

Multiply both sides by the common denominator:

 

12 * (15 - x) + 12 * (15 + x) = 1.67 * ((15 + x) * (15 - x))

 

Clear parenthesis:

 

180 - 15x + 180 + 15x = 1.67 * (225 - 15x + 15x - x²)

 

360 = 1.67 * (225 - x²)

 

Divide both sides by 1.67:

 

360 / 1.67 = 225 - x²

 

Multiply the equation by -1:

 

-360 / 1.67 = -225 + x²

 

Add 225 to both sides and rearrange:

 

x² = 225 - 360 / 1.67

 

x² = 9.43

 

Find the square root of x:

 

x = ±3.07

 

The solutions are x = 3.07 and x = -3.07. We can discard x = -3.07 because water normally does not run back up stream. That means the stream is flowing at a rate of 3.07 kmp.

 

Check:

 

12 / (15 + 3.07) + 12 / (15 - 3.07) = 1.67

 

12 / 18.07 + 12 / 11.97 = 1.67

 

.66 + 1.01 = 1.67

 

1.67 = 1.67, values check.

 

 

Questions?