A river boat - Math Central

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Question from jessica, a student:

here's a crazy riddle a river boat that travels 12 mph in still water makes a pleasure trip to a city upstream and back in 3 hours. If the city is 10 miles away, what is the rate of the current

The problem I am having is do I use time/distance i am confused

Thanks=)

Hi Jessica.

You want to know the rate of the current, so let's call it R.

On the way to the city (upstream), the boat is fighting the current, so its effective speed is R-12.
Since distance divided by speed equals time, this means it takes 10 / (R-12) hours to get to the city.

On the way back (downstream), the boat is going with the current, so its effective speed is R+12.
Thus it takes 10 / (R+12) hours to return from the city.

The total time is 3 hours, which equals the sum of the time going to the city and the time returning:

3 = [ 10 / (R-12) ] + [ 10 / (R+12) ]

Solve for R.

Cheers,
Stephen La Rocque.

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