A bear loves visiting his friend, the piglet. The distance between their houses is 300m , and the bear always walks from his house to the piglet's house in exactly the same amount of time. But today, the bear stops at a beehive after walking —1 of the 4 distance. He eats honey for 2.5 minutes and then continues to the piglet's house at a speed 15 m/min faster than usual. The total journey to the piglet's house takes the exact same amount of time as it usually does, when the bear does not stop for honey. How long does the journey take?

10mins

Step-by-step explanation:

you can draw a rtd chart for this problem

             rate (m/min)|  time (mins)  | distance (m )

regular: (300/x)  | x  | 300m

fist 1/4 : (300/x) | 75: (300/x)  | 75m

last 3/4:  | (300/x)+15 | 225:(300/x + 15) | 225m

then, make an equation for the times:

x= (75: (300/x)) + (225: ( (300/x)+15) + 2.5 = x

// get the 2.5 mins from the stop for honey, and we know that regular speed is equal to the one with a stop

solve equation to get x=-20/3 , x=10, because speed is positive, x=10 is the most reasonable answer

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)