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January 20th, 2013, 12:02 PM  #1 
Member Joined: Feb 2012 Posts: 78 Thanks: 0  Help setting up problem
A boat can reach its destination in 3 hours. If it goes twice as fast, it can reach 10 miles more than its destination, in 2 hours. How fast does it originally go? The answer is 10 mph. But how should I set this problem up to figure out? I know Distance = Rate x Time. 
January 20th, 2013, 12:09 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Help setting up problem
Let be the original speed. If it can reach the destination at this speed in 3 hours, then we may write: If the speed is doubled, and it can go 10 miles more than d in 2 hours, then we may also write: Now, if we subtract the first equation from the second, we eliminate d to obtain: So we know the original speed is 10 mph. 
January 20th, 2013, 12:29 PM  #3 
Member Joined: Feb 2012 Posts: 78 Thanks: 0  Re: Help setting up problem
Another question I have is A man can drive a certain distance in 5 hours. If he increased his speed by 10mph, he could travel the same distance in 41/6 hours. What is the distance he travels? The answer is 250 miles. The way I set it up is He can drive a certain distance in 5 hours. So d=5r and d=(10+r)19/6 I'm pretty sure I set that up wrong too. Any help would be appreciated :P 
January 20th, 2013, 12:45 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Help setting up problem
You have the right approach, but . However, I can see from working the problem you want the time at the increased speed to be , and so you have: So, multiply the first equation by 5, then add to the second to get: 
January 20th, 2013, 03:14 PM  #5  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Help setting up problem Quote:
Quote:
 

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