Question

The time taken for covering a distance of 'x' by downstream is equal to covering distance 'x–18'
by upstream. Upstream speed is less than 8 km./hr than that of downstream. If the speed of boat
in still water is 16 km/hr. Find the value of x

Answer 1

Answer:

The value of x is 45 km

Step-by-step explanation:

Speed of boat in still water = 16 km/hr

Let the speed of the stream be v km/hr

∴ Upstream speed of the boat = (16-v) km/hr

And, Downstream speed of the boat = (16+v) km/hr

According to the question

$(16+v)-(16-v)=8$

$\implies 2v=8$

$\implies v=4 \text{km/hr}$

Therefore,

Upstream speed of the boat = 12 km/hr

Downstream speed of the boat = 20 km/hr

Time taken to cover the distance x in downstream direction = x/20 hr

Time taken to cover the distance x-18 in upstream direction = (x-18)/12 hr

According to the question

$\frac{x}{20} =\frac{(x-18)}{12}$

$\implies \frac{x}{5} =\frac{(x-18)}{3}$

$\implies 3x=5x-(18\times5)$

$\implies 2x=18\times5$

$\implies x=9\times5$

$\implies x=45$