Questions: From a parking lot, a person wants to walk to a house on the ocean. The house is located 1800 feet down a paved path that parallels the beach, which is 600 feet wide as shown in the figure. Along the path he can walk 450 feet per minute, but in the sand on the beach he can only walk 150 feet per minute. Complete parts (a) through (g). Ocean (a) Calculate the time T if he walks 1800 feet along the paved path and then 600 feet in the sand to the house. T=8 minutes (Type an integer or decimal rounded to one decimal place as needed.) (b) Calculate the time T if he walks in the sand directly toward the ocean for 600 feet and then turns left and walks along the beach for 1800 feet to the house. T= (Type an integer or decimal rounded to one decimal place as needed.)

From a parking lot, a person wants to walk to a house on the ocean. The house is located 1800 feet down a paved path that parallels the beach, which is 600 feet wide as shown in the figure. Along the path he can walk 450 feet per minute, but in the sand on the beach he can only walk 150 feet per minute. Complete parts (a) through (g).

Ocean
(a) Calculate the time T if he walks 1800 feet along the paved path and then 600 feet in the sand to the house.
T=8 minutes
(Type an integer or decimal rounded to one decimal place as needed.)
(b) Calculate the time T if he walks in the sand directly toward the ocean for 600 feet and then turns left and walks along the beach for 1800 feet to the house.
T= 
(Type an integer or decimal rounded to one decimal place as needed.)
Transcript text: From a parking lot, a person wants to walk to a house on the ocean. The house is located 1800 feet down a paved path that parallels the beach, which is 600 feet wide as shown in the figure. Along the path he can walk 450 feet per minute, but in the sand on the beach he can only walk 150 feet per minute. Complete parts (a) through (g). Ocean (a) Calculate the time T if he walks 1800 feet along the paved path and then 600 feet in the sand to the house. $\mathrm{T}=8$ minutes (Type an integer or decimal rounded to one decimal place as needed.) (b) Calculate the time $T$ if he walks in the sand directly toward the ocean for 600 feet and then turns left and walks along the beach for 1800 feet to the house. $\mathrm{T}=$ $\square$ minutes (Type an integer or decimal rounded to one decimal place as needed.)
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Solution

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(a) Calculate the time T if he walks 1800 feet along the paved path and then 600 feet in the sand to the house.

Time on paved path

Time = Distance / Speed Time = 1800 feet / 450 feet/minute Time = 4 minutes

Time on sand

Time = Distance / Speed Time = 600 feet / 150 feet/minute Time = 4 minutes

Total time

Total time = Time on paved path + Time on sand Total time = 4 minutes + 4 minutes Total time = 8 minutes

\( \boxed{8} \) minutes

(b) Calculate the time $T$ if he walks in the sand directly toward the ocean for 600 feet and then turns left and walks along the beach for 1800 feet to the house.

Time in sand

Time = Distance / Speed Time = 600 feet / 150 feet/minute Time = 4 minutes

Time along the beach

Time = Distance / Speed Time = 1800 feet / 150 feet/minute Time = 12 minutes

Total time

Total time = Time in sand + Time along the beach Total time = 4 minutes + 12 minutes Total time = 16 minutes

\( \boxed{16} \) minutes

8 minutes 16 minutes

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