SOLUTION: Two cyclists start from the same point and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hr, they are 126 mi apart. Find the rate of each cyclist
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Question 1196996: Two cyclists start from the same point and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hr, they are 126 mi apart. Find the rate of each cyclist.
Slower cyclist _______=MPH
Faster cyclist _______=MPH
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
x = speed of the slower cyclist
2x = speed of the faster cyclist (traveling twice as fast)
speeds are in miles per hour (mph)
The variable x is a placeholder for some positive real number
After 3 hours, we have these respective distances traveled
slower = 3x
faster = 3*2x = 6x
I used the formula distance = rate*time
These two distances must add to the 126 miles.
You could draw out a diagram like shown below to help visualize what's happening.
Once you get used to problems like this, the diagram becomes optional in my opinion. But it's helpful to draw out a diagram whenever you get stuck.
They both start at point A
The slower cyclist goes to point B, traveling 3x miles
The faster cyclist goes to point C, traveling 6x miles
The distance from B to C is 126 miles, aka 3x+6x
(slower cyclist's distance) + (faster cyclist's distance) = 126
(3x)+(6x) = 126
9x = 126
x = 126/9
x = 14
which is the slower cyclist's speed
and 2x = 2*14 = 28 mph is the faster cyclist's speed
The slower cyclist travels for 3*14 = 42 miles
The faster cyclist travels for 3*28 = 84 miles
Note: the faster cyclist travels twice as far
The total distance is 42+84 = 126 miles which helps fully verify our answers.
Answer:
Slower cyclist = 14 mph
Faster cyclist = 28 mph
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