Am completely stuck on this one, so am having a hard time explaining the step-by-step instructions for solving the problem below. Help would be greatly appreciated.
Two travelers are 220 kilometers apart at noon and are headed toward each other along a straight road. They meet at 5:30 PM, and one traveled 20 kilometers per hour faster than the other. What is the speed of the faster traveler?
When did they leave? One has to have time, or velocity given.
The problem only indicates that they are 220 kilometers apart at noon.
Each traveled 5.5 hours
I made a chart
..........Distance....rate........time
trav#1......5.5x......x km/h.....5.5 hrs
trav#2....5.5(x+20)...x+20 km/h..5.5 hrs
...total...220
so 5.5x + 5.5(x+20) = 220
solve, it is easy from here on.
(I got 30 km/h)
Thank you very much!
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Homework Help Forum: Math - Algebra
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Posted by Hunter on Friday, October 12, 2007 at 9:55pm.
Am completely stuck on this one, so am having a hard time explaining the step-by-step instructions for solving the problem below. Help would be greatly appreciated.
Two travelers are 220 kilometers apart at noon and are headed toward each other along a straight road. They meet at 5:30 PM, and one traveled 20 kilometers per hour faster than the other. What is the speed of the faster traveler?
They are 220km apart and approaching one another at the combined speed of V + (V + 20) = 2V + 20.
Therefore,from V = D/T, 220 /(2V + 20) = 5.5 which leads to 220 = 11V += 110 fromw which 11V = 110 and V = 10 making the faser speed 30 km/hr.
To find the speed of the faster traveler, we need to use the concept of relative speed.
Step 1: Understand the problem
The problem states that two travelers are 220 kilometers apart at noon and meet at 5:30 PM. This means they have been traveling for 5 hours and 30 minutes. One traveler is going 20 kilometers per hour faster than the other.
Step 2: Set up the equation
Let's assume the speed of the slower traveler is x kilometers per hour. Therefore, the speed of the faster traveler would be x + 20 kilometers per hour. We can now set up the equation using the formula Time = Distance / Speed:
5.5 hours = 220 kilometers / (x + x + 20) kilometers per hour
Step 3: Simplify the equation
To simplify the equation, we can multiply both sides by (x + x + 20). This will eliminate the denominator on the right side.
5.5 hours * (x + x + 20) = 220 kilometers
Step 4: Solve the equation
Distribute the 5.5 hours across the terms on the left side of the equation:
5.5x + 5.5x + 110 = 220
Combine like terms:
11x + 110 = 220
Subtract 110 from both sides:
11x = 110
Divide both sides by 11:
x = 10
Step 5: Find the speed of the faster traveler
Since we assumed the speed of the slower traveler (x) is 10 kilometers per hour, the speed of the faster traveler (x + 20) would be:
10 + 20 = 30 kilometers per hour
Therefore, the speed of the faster traveler is 30 kilometers per hour.