Question

a motar boat has a speed of 15 km per hour in still water the motar boat goes 30 km downstream at coens back in a total of 4 hours and 30 minutes the speed of the current river is
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Answer 1

Answer: 5km/h

Explanation:

let speed of stream be y km/h

if the boat has speed 15km/h in still water then speed of boat down stream is 15+y  and upstream is 15-y.

time taken to go down is 30/(15+y)

time taken to go up is 30/(15-y)

total time taken is 4.5 hour

30/(15+y) + 30/(15-y) = 4.5

solving this give y= 5  ( if u need the solution of equation comment below)

hope this help

if good mark brainliest

Answer 2

Answer :

The speed of the current of the river is 5km/h

Given :

• The speed of the motor in still water is 15km/h
• The motor boat goes 30km downstream and comes back in a total of 4 hours 30mins or 4.5 hours

Solution :

Let us consider the speed of the current of river be x km/h

The speed of the bo boat in downstream is

(15 +x) km/h and the speed at upstream is

(15 - x)km/h

Now

$\sf{speed = \dfrac{distance}{time} } \\ \\ \implies \sf{time = \dfrac{distance}{time} }$

The time taken to go upstream

$\sf \longrightarrow \dfrac{30}{15 - x} \: \: \: hr$

Similarly , time taken to go downstream

$\sf \longrightarrow \dfrac{30}{15 + x} \: \: hr$

$\dag \sf{ \: According \: \:to \: \: question }$

$\sf{ \dfrac{30}{15 - x} + \dfrac{30}{15 + x} } = 4.5 \\ \\ \implies \sf \dfrac{30(15 + x) + 30(15 - x)}{(15 + x)(15 - x)} = \frac{45}{10} \\ \\ \implies \sf30 \times 10(15 + x + 15 - x) = 45(15 + x)(15 - x) \\ \\ \implies \sf \dfrac{30 \times 10}{45} \times 30 = 15 ^{2} - x {}^{2} \\ \\ \sf\implies200 = 225 - {x}^{2} \\ \\ \sf\implies - {x}^{2} = 200 - 225 \\ \\ \sf \implies - {x}^{2} = - 25 \\ \\ \implies \sf {x}^{2} = 25 \\ \\ \implies \boxed{\sf{x = 5}}$

The speed of the river current is 5km/h