SOLUTION: A troop of scouts hike to the scout cabin at the rate of 2 miles per hour. They ride back to headquarters at 18 miles per hour. If the round trip takes 10 hours, how far is headqua

Question 835124: A troop of scouts hike to the scout cabin at the rate of 2 miles per hour. They ride back to headquarters at 18 miles per hour. If the round trip takes 10 hours, how far is headquarters from the cabin?
This is the equation I found. However, I don't understand where the nine came from or why their dividing the distance.
(d/2) + (d/18) = 10
(9d/18) + (d/18) = 10
10d/18 = 10
d=18 miles
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A troop of scouts hike to the scout cabin at the rate of 2 miles per hour. They ride back to headquarters at 18 miles per hour. If the round trip takes 10 hours, how far is headquarters from the cabin?
This is the equation I found. However, I don't understand where the nine came from or why their dividing the distance.
---------
Equation:
time = distance/rate
time + time = time
(d/2) + (d/18) = 10 hrs
----
d/2 = (9/9)(d/2) = 9d/18
--------------
(9d/18) + (d/18) = 10
10d/18 = 10
d=18 miles
------
Cheers,
Stan H.
---------------
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
d/2=9d/18 because 1/2*d=9/18*d
r*t=d
t=d/r
t=d/2
t=d/18
total time is 10 so add the two time parts of the round trip to get the total time
so from the beginning
d/2+d/18=10
find common denominator which is 18
1/2*d=9/18*d
9/18*d+d/18=10
10/18*d=10
divide by 10
d/18=1
d=18

RELATED QUESTIONS
A scout troop hiked 3 miles up a mountain trail. They then hiked back down the same... (answered by mananth)
I need help solving this problem. I am not quite sure how to set it up. The campers... (answered by gonzo)
A troop of scouts hiked to the city at a rate of 2 mph. they rode back at a rate of 18... (answered by yuvaraja)
Scouts in troop 2 can hike at an average speed of 2 1/2 mph. At that rate how far an the (answered by rfer)
Ronold rode away from home in a car at the rate of 32 miles per hour. he walked back at... (answered by jorel555)
Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail... (answered by Theo,josgarithmetic)
Please help me solve this word problem. Sat Tranh took a short hike with his friends up... (answered by josgarithmetic,stanbon)
A boy rides away from home in an automobile at a rate of 28 miles per hour and walks back (answered by greenestamps,Alan3354)
Ronald rode away from home in a car at rate of 32 miles per hour. He walked back at the... (answered by Alan3354)