Question

a motor boat whose speed is 12 km/hr in still water takes 2hours less to go 45km down stream than to return up stream to the same spot . find the speed of the current
i will make you as brainlist

Answer 1

ANSWER

The speed of the current is 3km/h

GIVEN

• A motor boat has a speed of 12km/h in still water
• It takes 2 hours less to go 45km downstream than to return upstream.

FORMULA TO BE USED

• Speed = Distance/time

SOLUTION

Let us consider the speed of current be x km/h

Also let the time taken in downstream be t hours and upstream be (t - 2)hours

We know that ,

$\tt speed = \dfrac{distance}{time} \\ \\ \dashrightarrow \tt time = \dfrac{distance}{speed}$

Considering the downstream :

$\tt \implies t = \dfrac{45}{12 + x} \: \longrightarrow(1)$

And considering the upstream :

$\tt \implies t + 2 = \dfrac{45}{12 - x} \: \longrightarrow(2)$

Subtracting (1) from (2) we have :

$\implies \tt t + 2 - t = \dfrac{45}{12 - x} - \dfrac{45}{12 + x} \\ \\ \implies \tt 2 = \dfrac{45(12 + x) - 45(12 - x)}{(12 - x)(12 + x)} \\ \\ \implies \tt2 = \dfrac{45(12 + x - 12 + x)}{12 {}^{2} - {x}^{2} } \\ \\ \implies \tt2 = \dfrac{45 \times 2x}{144 - {x}^{2} } \\ \\ \implies \tt1 = \frac{45x}{144 - {x}^{2} } \\ \\ \implies \tt144 - {x}^{2} = 45x \\ \\ \implies \tt{x}^{2} + 45x - 144 = 0 \\ \\ \implies \tt {x}^{2} + 48x - 3x - 144 = 0 \\ \\ \implies \tt x(x + 48) - 3(x + 48) = 0 \\ \\ \implies \tt(x - 3)(x + 48) = 0$

Now we have ,

$\tt \implies x - 3 = 0 \: \: and \: \implies x + 48 = 0 \\ \\ \tt \implies x = 3 \: \: and \: \: \implies x = - 48$

Since , speed can never be negative so the x≠-48

Thus , the speed of the current is 3km/h