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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: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Help setting up problem Let $v$ be the original speed. If it can reach the destination at this speed in 3 hours, then we may write: $d=3v$ If the speed is doubled, and it can go 10 miles more than d in 2 hours, then we may also write: $d+10=2(2v)=4v$ Now, if we subtract the first equation from the second, we eliminate d to obtain: $10=v$ 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 4-1/6 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: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Help setting up problem You have the right approach, but $4-\frac{1}{6}=\frac{24-1}{6}=\frac{23}{6}$. However, I can see from working the problem you want the time at the increased speed to be $4+\frac{1}{6}=\frac{24+1}{6}=\frac{25}{6}$, and so you have: $d=5r$ $d=\frac{25}{6}(r+10)\,\therefore\,6d=25r+250$ So, multiply the first equation by -5, then add to the second to get: $d=250$
January 20th, 2013, 03:14 PM   #5
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Re: Help setting up problem

Quote:
 Originally Posted by swm06 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 4-1/6 hours.
Is this "4 minus 1/6" hours (23/6 hours) as MarkFL assumed or is it "4 and 1/6" hours, which would be 25/6 hours?

Quote:
 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

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