A motorboat travels 165 Kilometers in 5 hours going

Ответ:

StrawberryCake24

19.01.2022

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

Solution:

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

Find upstream speed:

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

Thus upstream speed is 33 km per hour

Downstream distance = 305 km

Downstream time = 5 hours

Find downstream speed:

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

Thus downstream speed is 61 km per hour

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

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 61 ---- eqn 1

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

Add eqn 1 and eqn 2

u + v + u - v = 61 + 33

2u = 94

u = 47

Substitute u = 47 in eqn 1

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

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