Question

A boat takes 20 hours to travel downstream from point p to point q and coming back to a point r midway between p and q. If the velocity of the stream is 5 kmph and the speed of the boat in still water is 13 kmph, then what is the distance between p and q?

Answer 1

$\Huge{\textbf{Answer}}$

PQ = 122.4 km

$\Huge{\textbf{Explanation}}$

Given

vb = 13 km/h

vs = 5 km/h

t = 20 h

$\Huge{\textbf{Solution}}$

Relative velocity of boat downstream -

vd = vs + vb

vd = 5 + 13

vd = 18 km/h

Relative velocity of boat against stream-

vu = vb - vs

vu = 13 - 5

vu = 8 km/h

Let s be the distance between P to Q, then

s/8 + 0.5s/13 = 20

(13s + 4s) / 104 = 20

17s = 2080

s = 122.4 km

Distance between P to Q is 122.4 km.

Answer 2

Answer:

169.4

Explanation:

Let x be the distance between P and Q

thus distance between P an R will be x/2  since r is inn the middle of P and Q  

x/u+v  + x/2/u-v  = 20

x/13+5  +  x/2/13-5 =20

x/18 +x/16 =20

8x+9x/144 =20

17x/144 =20

x=20*144/17

=169.4