A motorboat travels 165 Kilometers in 5 hours going up stream. It travels 305 kilometers going downstream in the same amount of

Question

3 years ago

5

time. What is the rate of the boat in still water and what is the rate of the current

1 answer:

Serhud [2] · Answer 1 · 2022-07-08T16:29:57+03:00

<h2>Rate of the boat in still water is 47 km/hr and rate of the current is 14 km/hr</h2>

<em><u>Solution:</u></em>

Given that,

A motorboat travels 165 Kilometers in 5 hours going up stream.

It travels 305 kilometers going downstream in the same amount of time

Therefore,

Upstream distance = 165 km

Upstream time = 5 hours

<h3><u>Find upstream speed:</u></h3>

$speed = \frac{distance}{time}\\\\speed = \frac{165}{5}\\\\speed = 33$

Thus upstream speed is 33 km per hour

Downstream distance = 305 km

Downstream time = 5 hours

<h3><u>Find downstream speed:</u></h3>

$speed = \frac{305}{5}\\\\speed = 61$

Thus downstream speed is 61 km per hour

<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then </u></em>

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 61 ---- eqn 1

u - v = 33 ----- eqn 2

u + v + u - v = 61 + 33

2u = 94

u = 47

<em><u>Substitute u = 47 in eqn 1</u></em>

47 + v = 61

v = 61 - 47

v = 14

Thus rate of the boat in still water is 47 km/hr and rate of the current is 14 km/hr