# How do you solve this word problem?

The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to B, how long does it take him to make the return trip from B to A?

Please explain the steps :) thankyou

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First, use what you are given about the time taken to travel from $A$ to $B$, and the given rates, to compute the distance $d$ between $A$ and $B$:

$$d = 1.25\;\text{hours}\;\cdot \left(\frac {15\;\text{miles}}{1\;\text{hour}} + \frac{45\;\text{miles}}{1\;\text{hour}}\right)$$

Above, we add the rate at which the river is moving to the rate at which the boat moves on still water, to get the overall rate at which the boat is traveling from point A to point B. (It's traveling with the current).

Then, try setting up the equation you need to solve for the time needed to travel distance $d$ from point $B$ to point $A$ at a rate of $(45\; \text{mph}\;- 15\;\text{mph})$. Here, we subtract the rate of the current, which is going in the opposite direction than the boat is, from the rate of movement of the boat in still water.

Try to set up the equation and then solving for the unknown, but desired time needed to travel from point B to point A. I'll be happy to check your progress, if you follow up in the comments below.

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Distance is 75 miles. Based on d = r * t equation, t = 75 / (45 - 15) so t = 75 / 30 which equals to 2.5 hours, right? I think part of the problem was I couldn't picture the problem in my head, and your answer helped, thanks! – anita Jun 27 '13 at 22:22
Exactly! Good work. – amWhy Jun 27 '13 at 22:24
@amWhy: The sort of feedback I love! +1 – Amzoti Jun 28 '13 at 2:36
Yes, it's great to get that kind of feedback. What some users here don't seem to understand is that some students are very timid about sharing what they know, and don't...so I debated about how much to say...glad I let the OP have a chance to show his/her stuff! – amWhy Jun 28 '13 at 2:38
${\cdots}{+1}{\cdots}{+1}{\cdots}{+1}{\cdots}{}$ – Babak S. Jul 5 '13 at 6:34

Hint: what is the speed of the boat from A to B? what is the speed of the boat from B to A?

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