Question

Two men p and q start from two points x and y on opposite banks of a still river towards y and x respectively .They meet at 340 m from one bank x and proceed on their respective onward journey. After that they meet at 170 m from the bank y on their return journey. What is tje width of the river

Answer 1

Answer:

The width of the river is 850 m

Step-by-step explanation:

Let the speeds of P and Q be u and v respectively

Let the width of the river be W

Then

As P starts from X and Q starts from Y and they meet at 340 m from X

If the time is t then

340 = ut

or t = 340/u

Also

W-340 = vt

or, (W - 340) = 340v/u

or, u/v = 340/(W - 340)  .......... (i)

Again

when they meet at 170 m from bank Y, the distance traveled by P will be W + 170 and distance traveled by Q will be 2W - 170

If the time taken from the start of the journey is t' then

(W + 170)/u = t'

And (2W - 170)/v = t'

Thus

(W + 170)/u = (2W - 170)/v

or (W + 170)/(2W - 170) = u/v ........... (ii)

From eq (i) and eq (ii)

$\frac{340}{W-340} =\frac{W+170}{2W-170}$

$\implies 340(2W-170)=(W+170)(W-340)$

$\implies 680W-57800=W^2-170W-57800$

$\implies 850W-W^2=0$

$\implies W(W-850)=0$

$\implies W=0, 850$

but the width of the river cannot be 0

Therefore, W = 850 m