Let x be rate of boat in still water
let y be rate of current

we use this equation to relate quantities:
distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream
144 = 3(x-y)
144 = 3x - 3y

for downstream
144 = 2(x+y)
72 = x + y

system of eqns:
144 = 3x - 3y
72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h
rate of the current is 12 km/h

6 0

2 years ago

A fair coin is flipped twice. Drag letters to complete the tree diagram to represent the sample space

ankoles [38]

Answer:

Step-by-step explanation:

6 0

2 years ago

The volume of a large can of tuna fish can be calculated using the formula V= πr(r)h. Write an equation to find the radius, r, i

noname [10]

The equation $r=\sqrt\frac{V}{3.14h}$ can be used to find the radius.

Step-by-step explanation:

Given,

Volume of large can;

V=πr(r)h

V=πr²h

Dividing both sides by πh

$\frac{V}{\pi h}=\frac{r^2\pi h}{\pi h}\\\\\frac{V}{\pi h}=r^2\\\\r^2=\frac{V}{\pi h}$

Taking square root on both sides

$\sqrt{r^2}=\sqrt{\frac{V}{\pi h}}\\r=\sqrt\frac{V}{\pi h}$

Putting π=3.14

$r=\sqrt\frac{V}{3.14h}$

The equation $r=\sqrt\frac{V}{3.14h}$ can be used to find the radius.

Keywords: volume, square root

Learn more about square root at:

#LearnwithBrainly

5 0

2 years ago

Three friends are playing catch. Zoe is in a straight path 12 feet to the west of alex. Jin is in a straight path 9feet to the n

Tanzania [10]

Answer:

15 ft

Step-by-step explanation:

This problem can be represented by a right angle triangle, shown in the diagram below.

The distance between Jin and Zoe is the hypotenuse of the triangle, x.

According to Pythagoras theorem,

hyp² = opp² + adj²

Where opp is the opposite side and adjacent is the adjacent side to any angle of consideration (which is not important in this case)

Hence:

x² = 12² + 9²

x² = 144 + 81

x² = 225

Finding the square root:

x = 15 ft

Jin and Zoe are 15 ft apart.

4 0

2 years ago