Question

A man rows a boat at a speed of 15 mph in still water. find the speed of the river if it takes her 4 hours 30 minutes to row a boat to a place 30 miles away and return.

Answer 1

here
va=15mph
d=30miles
t=4hours 30 min=4.5hours
we know
t=d÷sqrt(va2-vb2)
4.5=30÷sqrt(225-vb2)
vb2=180.56
vb=sqrt(180.56)

Answer 2

Answer:

The speed of water is 5 mph.

Step-by-step explanation:

Let the speed of water be x.

The speed of boat in still water is 15 mph.

The speed in upstream is 15-x. The speed in downstream is 15+x.

It is given that it takes her 4 hours 30 minutes to row a boat to a place 30 miles away and return.

4 hours 30 minutes = $4\frac{30}{60}=4\frac{1}{2}=\frac{9}{2}$

$Time=\frac{Distance}{Speed}$

$\frac{30}{15-x}+\frac{30}{15+x}=\frac{9}{2}$

$\frac{-900}{x^2-225}=\frac{9}{2}$

$-200=x^2-225$

$25=x^2$

$x=\pm 5$

The speed cannot be negative.

Therefore the speed of water is 5 mph.