Question

Prince Ivan rides gray wolf and a constant speed from kings castle to the magic apple garden in five hours. on the return trip to kings castle gray wolf runs at that original constant speed for the first 36 km then runs the rest of the way 3 km/h faster. what was grey Wolf original speed if the return trip took 15 minutes less than the trip from kings castle to magic apple garden? (List what the original speed of grey wolf can be)

Answer 1

Answer:9 km/h or 48 km/h

Step-by-step explanation:

Let the distance is d, speed is s

As per given we have:

d/s = 5

36/s + (d - 36)/(s + 3) = 5 - 1/4

Substitute d with 5s and solve for s:

36/s + (5s - 36)/(s + 3) = 19/4

36(s + 3) + s(5s - 36) = 19s(s + 3)/4

4(36s + 108 + 5s² - 36s) = 19s² + 57s

20s² + 432 = 19s² + 57s

s² - 57s + 432 = 0

s² - 9s - 48s + 432 = 0

s(s - 9) - 48(s - 9) = 0

(s - 9)(s - 48) = 0

s -9 = 0 ⇒ s = 9 km/h

s - 48 = 0 ⇒ s = 48  km/h

The original speed of grey wolf can be 9 km/h or 48 km/h

Step-by-step explanation:

Answer 2

Answer:

• 9 km/h or 48 km/h

Step-by-step explanation:

• Let the distance is d, speed is s

As per given we have:

• d/s = 5
• 36/s + (d - 36)/(s + 3) = 5 - 1/4

Substitute d with 5s and solve for s:

• 36/s + (5s - 36)/(s + 3) = 19/4
• 36(s + 3) + s(5s - 36) = 19s(s + 3)/4
• 4(36s + 108 + 5s² - 36s) = 19s² + 57s
• 20s² + 432 = 19s² + 57s
• s² - 57s + 432 = 0
• s² - 9s - 48s + 432 = 0
• s(s - 9) - 48(s - 9) = 0
• (s - 9)(s - 48) = 0

• s -9 = 0 ⇒ s = 9 km/h
• s - 48 = 0 ⇒ s = 48  km/h

The original speed of grey wolf can be 9 km/h or 48 km/h