Benito and Tyler are painting opposite sides of a 150-foot fence. Tyler has already paint 39/2 ft of his side when Benito gets started. Benito is painting at a rate of 15 ft/min, while Tyler is moving slower at 11 ft/min.

Question

Benito and Tyler are painting opposite sides of a  150-foot fence. Tyler has already paint 39/2 ft of his side when Benito gets started. Benito is painting at a rate of 15 ft/min, while Tyler is  moving slower at 11 ft/min.
a. Write and solve an equation to determine how long it will take for the two sides of the fence to have an equal number of feet painted? How many feet will be on Benito's side of the fence when the two sides have an equal number of feet painted?
b. Tyler claims that because he started first, he will finish painting his side of the fence before Benito finishes painting his side. is this true? Explain using mathematical evidence.
c. The painter  who finishes first gets to rest while the other painter finishes. How long will the painter who finishes  first get to rest? Explain.

oobleck · Answer

(a) 15t = 39/2 + 11t
(b) Solve (a) for t. If t <= 10 then Benito has not painted his whole side.
(c) the winner will get to rest for x/s hours, where x is the amount of fence still unpainted by the loser, and y is the loser's speed.