Question

A boat goes downstream and covers the
distance between two ports in 4 hours. It
covers the same distance in 6 hours when it
goes upstream. If speed of boat is 5 km/h,
then find the speed of water.​

Answer 1

$\bold{\underline{\underline{Assume\::}}}$

Let the -

• Distance between two ports be "D" km.

• Speed of boat in water be "S" km/hr.

$\bold{\underline{\underline{Solution\::}}}$

→ Speed of boat = 5 km/hr.

A boat goes downstream and covers the

distance between two ports in 4 hours.

→ Speed of boat down the string = (S + 5) km/hr

→ Time = 4 hrs.

$\bold{Time\:=\:\dfrac{Distance}{Velocity}}$

Substitute the known values in above formula

$\implies\:4\:=\:\dfrac{D}{S\:+\:5}$ ___ (eq 1)

Boat covers the same distance in 6 hours when it goes upstream.

→ For upstream speed = (S - 5) km/hr.

→ Time = 6 hrs.

$\implies\:6\:=\:\dfrac{D}{S\:-\:5}$ ___ (eq 2)

Now,

Divide (eq 1) by (eq 2)

$\implies\:\dfrac{4}{6}\:=\:\dfrac{ \frac{D}{S \: + \: 5} }{ \frac{D}{S \: - \: 5} }$

$\implies\:\dfrac{4}{6}\:=\:\dfrac{S\:-\:5}{S\:+\:5}$

Cross-multiply them

$\implies\:4(S\:+\:5)\:=\:6(S\:-\:5)$

$\implies\:4S\:+\:20\:=\:6S\:-\:30$

$\implies\:4S\:-\:6S\:=\:-\:30\:-\:20$

$\implies\:-\:2S\:=\:-\:50$

$\implies\:S\:=\:25\:km/hr.$

(Speed of boat)

Substitute value of S in (eq 1)

$\implies\:4\:=\:\dfrac{D}{25\:+\:5}$

$\implies\:4\:=\:\dfrac{D}{30}$

$\implies\:D\:=\:120\:km$

(Distance between two ports)

∴ Speed of boat in water is 25 km/hr.