Question 176862: I need help solving this problem. I am not quite sure how to set it up.
The campers left headquarters hiking to a cabin at a rate of 2 mph. They rode back to headquarters at a rate of 18 mph. If the entire round trip took 10 hours, what is the distance from the cabin to headquarters?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! this is a rate * time = distance type of problem.
you have two formulas.
one is going from headquarters to the cabin.
the other is going from the cabin to headquarters.
the rate going is 2 mph.
the time it takes is t1.
the distance is d.
the formula going from headquarters to the cabin is.
2 * t1 = d
the rate coming back is 18 mph.
the time it takes is t2.
the distance is d (same distance as going).
the formula going from the cabin to headquarters is.
18 * t2 = d
since both these formulas equal to d, then they are equal to each other.
2 * t1 = 18 * t2
we also know that the round trip took 10 minutes, so we know that:
t1 + t2 = 10
we can solve for t1 in terms of t2 or we can solve for t2 in terms of t1.
let's use t1 in terms of t2.
t1 = 10 - t2
we substitute 10 - t2 for t1 in the equation 2 * t1 = 18 * t2
that equation becomes:
2 * (10 - t2) = 18 * t2
removing parentheses, this becomes:
20 - 2 * t2 = 18 * t2
adding 2 * t2 to both sides of the equation gets:
20 = 20 * t2
dividing both sides of this equation by 20 gets:
t2 = 1
if t2 = 1, then t1 = 9
our equation of:
2 * t1 = 18 * t2 becomes:
2 * 9 = 18 * 1 which is true so the values for t1 and t2 are good.
you are asked, however, to find the distance.
go back to either equation and it should yield the distance.
the first equation was:
2 * t1 = d
since t1 = 9, this becomes:
2 * 9 = d
d = 18
the second equation was:
18 * t2 = d
since t2 = 1, this becomes:
18 * 1 = d
d = 18
d = 18 in both cases.
the distance is 18 miles.
everything checks out so this answer is good.
2 * 9 = 18
18 * 1 = 18
distance is 18 miles is your answer.
please note that the small t looks like a plus sign.
they are different though.
this is the small t: t
this is the plus sign: +
the cross on the small t is higher.
the cross on the + sign is in the middle.
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