Question

The speed of a stream is 4 km/h. A boat can go 20 km downstream and 14 km upstream in 3 hours. What is the speed (in km/h) of the boat in still water?

• A. 12
• B. 9
• C. 6
• D. 5

Answer 1

Answer:

A. 12

Let the speed of the boat in still water be (v) km/h.
Stream speed = 4 km/h.

• Downstream speed = (v + 4)

• Upstream speed = (v - 4)

Given:
$\frac{20}{v+4} + \frac{14}{v-4} = 3$

Solving:

$20(v-4) + 14(v+4) = 3(v^2 - 16)$
$20v - 80 + 14v + 56 = 3v^2 - 48$
$34v - 24 = 3v^2 - 48$
$3v^2 - 34v - 24 = 0$

Now solve using:

$v = \frac{34 \pm 38}{6}$
$v = 12 \text{ or } -\frac{2}{3}$

Reject negative value.

Speed of the boat in still water = 12 km/h