### Brain Teasers

# Camping Trip

Gretchen and Henry decide to go camping on a river. From where they put their canoes in the water, they paddle upstream for 3 hours, only to realize that their campground is located downstream from their starting point. They immediately turn around, and paddle downstream for the next 5 hours.

That night, they get some rest, make some s'mores, and tell ghost stories. They wake up the next morning to get back on the river, and paddle back to their starting point, 26 miles upriver.

Henry, knowing that this river flows at a constant rate of 2 miles per hour, says, "There's no way we're getting back by nightfall."

Gretchen does some quick math with a stick in the dirt, and says, "If we paddle at the same constant rate we did yesterday, we'll be back in time for a 6:00 dinner."

What time are they leaving?

That night, they get some rest, make some s'mores, and tell ghost stories. They wake up the next morning to get back on the river, and paddle back to their starting point, 26 miles upriver.

Henry, knowing that this river flows at a constant rate of 2 miles per hour, says, "There's no way we're getting back by nightfall."

Gretchen does some quick math with a stick in the dirt, and says, "If we paddle at the same constant rate we did yesterday, we'll be back in time for a 6:00 dinner."

What time are they leaving?

### Hint

If they finished 26 miles downstream from their starting point, how fast would they paddle in standing water?### Answer

They are leaving at 9:20 in the morning.If you denote their speed in standing water as x (miles per hour), then their speed upstream is x-2 and their speed downstream is x+2. On day 1, they traveled a distance downstream of 5(x+2) - 3(x-2), which equalled 26 miles. Solving for x, we get x = 5 miles per hour.

Knowing that they then need to travel upstream for those 26 miles to get home, their speed will be 3 miles per hour (= 5 - 2). It will therefore take them 8 2/3 hours, or 8 hours and 40 minutes.

In order to be back to their starting point by 6:00 pm, they therefore have to leave at 9:20 am.

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