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January 20th, 2013, 11:02 AM   #1
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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.
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January 20th, 2013, 11:09 AM   #2
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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.
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January 20th, 2013, 11:29 AM   #3
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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
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January 20th, 2013, 11:45 AM   #4
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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:

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January 20th, 2013, 02:14 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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