The Gotemba walking trail up Mount Fuji is about 9km long. Walkers need to return from the 18km walk by 8pm. Toshi estimates that he can walk up the mountain at 1.5km/h on average, and down at twice that speed. These speeds take into account meal breaks and rest times. Using Toshi's estimated speeds, what is the latest time he can begin his walk so that he can return by 8pm?

Toshi must begin his walk at 11:00 AM in order that he can return by 8:00 PM.

Step-by-step explanation:

Since the Gotemba walking trail up Mount Fuji is about 9km long, and walkers need to return from the 18km walk by 8pm, if Toshi estimates that he can walk up the mountain at 1.5km / h on average, and down at twice that speed , these speeds taking into account meal breaks and rest times, to determine what is the latest time he can begin his walk so that he can return by 8pm the following calculation must be performed:

Climb: 1.5 km / h

Descent: 2 x 1.5 km / h = 3 km / h

Climb: 9 km / 1.5 km / h = 6 hours

Descent: 9km / 3 km / h = 3 hours

Total: 9 hours

8 PM = 20:00

20:00 - 09:00 = 11:00

Thus, Toshi must begin his walk at 11:00 AM in order that he can return by 8:00 PM.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80