Question

The speed of a stream is 9 km/h. A boat can go 56 km downstream and 28 km upstream in 7 hours. What is the speed (in km/h) of the boat in still water?

• A. 16
• B. 20
• C. 9
• D. 15

Answer 1

Answer:

D. 15

Let the speed of the boat in still water be b km/h.
Speed of stream = 9 km/h

• Downstream speed = (b + 9)

• Upstream speed = (b - 9)

Given total time = 7 hours:

$\frac{56}{b+9} + \frac{28}{b-9} = 7$

Multiply throughout by ((b+9)(b-9)):

$56(b-9) + 28(b+9) = 7(b^2 - 81)$

Simplify:

$56b - 504 + 28b + 252 = 7b^2 - 567$
$84b - 252 = 7b^2 - 567$
$7b^2 - 84b - 315 = 0$

Divide by 7:
$b^2 - 12b - 45 = 0$

Factor:

$(b - 15)(b + 3) = 0$
Reject negative value, so:

$b = 15$

Speed of the boat in still water = 15 km/h