Question

Sat Tranh took a short hike with his friends at hill . Each users They hiked a uphill at steady pace of 1.5 miles per hour and downhill at a rate of 4 miles per hour. If the time to climb the mountain took an hour more than the time to hike down, how long was the entire hike

Answer 1

Total time for the entire hike = 2.2 hours

Step-by-step explanation:

speed = distance/time

distance = speed (time)

SInce speed = rate, we replace speed with rate in our workings

Uphill:

rate = 1.5 miles per hour

time = 1 hour + the time to hike down

let the time to hike down = h

time to go uphill = 1 + h

distance = rate (time)

distance = 1.5(1 + h)

Downhill:

rate = 4 miles per hour

time = h

distance = 4(h)

Distance to go uphill = distance to go downhill

1.5(1 + h) = 4(h)

1.5 + 1.5h = 4h

1.5 = 4h - 1.5h

1.5 = 2.5h

h = 1.5/2.5

h = 0.6

time to hike down = 1 + h = 1 + 0.6

time to hike down = 1.6 hrs

time to hike up = h = 0.6 hrs

Total time for the entire hike = 1.6 + 0.6

Total time for the entire hike = 2.2 hours