Question

A boat can cover 10 km up the stream and 5 km down the stream in 6 hours. If the speed of the stream is 1.5 km/hr. find the speed of the boat in still water.

Answer 1

Distance up stream = 10km
and down stream = 5km
Total time is taken = 6hours
Speed of stream = 1.5km/hr
Let the speed of a boat in still water = x km/hr
According to the condition,

`(10)/(x - 1.5) + (5)/(x + 1.5)` = 6

⇒ 10x + 15 + 5x + 5x - 7.5 = 6(x - 15)(x + 15)
⇒ 15x + 7.5 = 6(x² - 2.25)
⇒ 15x + 7.5 = 6x² - 13.5
⇒ 6x² - 15x - 13.5 - 7.5
⇒ 6x² - 15x - 21 = 0
⇒ 2x² - 5x - 7 = 0     ...(Dividing by 3)

⇒ 2x² - 7x + 2x - 7 = 0  ...`{(2 xx (-7) = 14), (-14 = -7 xx 2),(-5 = -7 + 2):}`
⇒ x(2x - 7) + 1(2x - 7) = 0
⇒ (2x - 7)(x + 1) = 0
Either 2x - 7 = 0,
then 2x = 7

⇒ x = `(7)/(2)`
or
x + 1 = 0,
then x = -1
But it is not possible being negative
∴ x = `(7)/(2)` = 3.5
∴Speed of boat = 3.5km/hr.