Question

The speed of a stream is 6 km/h. A boat can go 56 km downstream and 39 km upstream in 7 hours. What is the speed (in km/h) of the boat in still water?

• A. 22
• B. 15
• C. 7
• D. 13

Answer 1

Answer:

B. 15

Let the speed of the boat in still water be ( x ) km/h.
Speed of stream = 6 km/h

Downstream speed = ( x + 6 )
Upstream speed = ( x - 6 )

Given:
$\frac{56}{x+6} + \frac{39}{x-6} = 7$

Solve:
$\frac{56(x-6) + 39(x+6)}{(x+6)(x-6)} = 7$

$\frac{56x - 336 + 39x + 234}{x^2 - 36} = 7$

$\frac{95x - 102}{x^2 - 36} = 7$

$95x - 102 = 7(x^2 - 36)$
$95x - 102 = 7x^2 - 252$

$7x^2 - 95x - 150 = 0$

Solve:

$7x^2 - 95x - 150 = 0$

Discriminant:

$D = 95^2 + 4 \cdot 7 \cdot 150 = 9025 + 4200 = 13225 = 115^2$

$x = \frac{95 \pm 115}{14}$
$x = \frac{210}{14} = 15 \quad (\text{positive value})$

Answer: 15 km/h