Name: Dale
Who are you: Parent

My Son and I are having a hard time with this question:

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hour, the rate of the river and the rate of the boat in still water respectively are ____?

Thank you for your help.


Hi Dale.

Let's call the rate of the current with respect to the land C miles per hour and the rate of the boat with respect to still water B miles per hour.

Remember that distance = speed times time.

Going downstream 72 miles for 3 hours, the current and the boat are working together, so the total speed is B+C. This means that 72 = (B+C) x 3.

Coming back upstream for 60 miles in 6 hours, the current works against the boat, so the total speed is B-C. This means that 60 = (B-C) x 6.

Now take both of these equations and turn them into equations that "solve for B":

72 = (B+C) x 3
so 24 = B + C
so B = 24 - C


60 = (B-C) x 6
so 10 = B - C
so B = 10 + C

Now we have two different expressions with C that both equal B. Since two things that equal a third thing must be equal to each other, that means

24 - C = 10 + C

From here, I am sure you can solve for C (the current speed) and then use this value in either one of the original equations to find B, the boat speed in still water.

Hope this helps,
Stephen La Rocque.