Two butterflies simultaneously leave an aster flowerbed and fly to a rose flowerbed. One butterfly flies 10 m/min faster than the other, and so lands on a rose 1 minute earlier. Find the speed of each butterfly of the flower beds are 560m apart.

10.77 m/min ; 11.77 m/min

Step-by-step explanation:

Given :

Distance between the beds = 560m

Let :

Speed of butterfly 1 = x

Speed of butterfly 2 = x + 10

Time taken by butterfly one = t

Time taken by butterfly 2 = t - 1

Recall:

Speed = distance / time

Butterfly 1 :

x = 560 / t

xt = 560

t = 560/x

Butterfly 2:

x + 10 = 560 / t - 1

(x + 10)(t - 1) = 560

xt - x + 10t - 10 = 560

560 - x + 10(560/x) - 10 = 560

560 - x + 5600/x - 10 = 560

-x² - 560x + 6150 = 0

Using quadratic equation solver ;

x = - 570.77

x = 10.77

Speed can't be negative

Speed

butterfly 1= 10.77 m/min

Butterfly 2 = 10.77 +1 = 11.77 m /min

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).