Question

Benito and Tyler are painting opposite sides of the same fence. Tyler has already painted 19 1/2 feet of his side of the fence when Benito starts painting. How long will it take for the two sides of the fence to have an equal number of feet painted? How many feet will be painted on Benito's side of the fence when the two sides have an equal number of feet painted.

Answer 1

Answer:

Explanation:
Let x be the number of minutes after which both sides have equal number of feet painted,
∵ One side of the fence is painted by Benito,
His speed = 15 ft/min
So, the number of feet painted in one side after x minutes = 15x,
Now, second side of the fence is painted by Taylor,
The feet he already painted = ,
Taylor's speed = 11 ft/min
Thus, the number of feet painted in second side after x minutes = ,




Hence, it will take minutes for both sides to have an equal number of feet painted.

Answer 2

Part A: The time it will take for both of them to painted equal number of feet is 4.875 minutes

The number of feet Benito will have painted when the two sides have equal length is 73.125 feet

Part B: It is not true that Tyler will finish painting his side of the fence before Benito finishes painting his

Part C: Time to rest is 1.864 minutes

Step-by-step explanation: The given information are;

The length of fence Tyler already painted when Benito started = 19 ¹/₂ feet

Benito paints 15 feet/minute

Tyler paints 11 feet/minute

Length of fence = 150 feet

Part A:

The time it will take for both of them to painted equal number of feet is given as follows;

11×t + 19.5 = 15×t

4×t = 19.5

t = 19.5/4= 4.875 minutes

The time it will take for both of them to painted equal number of feet = 4.875 minutes

The length Benito will have painted when the two sides have equal length = 15 × 4.875 = 73.125 feet

Part B: The time it will take Tyler to finish painting his side of the fence is given as follows;

11 × t + 19.5 = 150

t = (150 - 19.5)/11 ≈ 11.864 minutes

While the time it will take Benito to finish painting his side of the fence is given as follows;

15 × t = 150

t = 150/15 ≈ 10 minutes

Therefore it is not true that Tyler will finish painting his side of the fence before Benito finishes painting his

Part C: Given that Benito finishes before Tyler, the length of time Benito gets to rest is given as follows;

Time to rest = Time Tyler takes to finish - Time Benito takes to finish

Time to rest = 11.864 - 10 = 1.864 minutes.