Question 1189896: Two cyclists start at the same point and travel in opposite directions.
One cyclist travels 3 km faster than the other.
If the two cyclists are 90 kilometers apart after 2 hours, what is the rate of each cyclist?
Found 3 solutions by math_tutor2020, Theo, Alan3354:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
x = speed of the slower cyclist
x+3 = speed of the faster cyclist (since he or she travels 3 km/hr faster)
We'll use this formula
distance = rate*time
often abbreviated as
d = r*t
For the slower cyclist, we have this equation
d = r*t
d = x*t
Meanwhile, the faster cyclist has this distance equation
d = r*t
d = (x+3)*t
So x*t and (x+3)*t represents how far the slower and faster cyclist traveled in that order.
Since they start at the same point, and travel in opposite directions, this means adding the two said expressions will yield the total distance they are apart.
distance between cyclists = x*t + (x+3)*t
Set that equal to the desired 90 km, and also plug in t = 2 to represent 2 hours. Solve for x.
x*t + (x+3)*t = 90
x*2 + (x+3)*2 = 90
2x + 2x+6 = 90
4x+6 = 90
4x = 90-6
4x = 84
x = 84/4
x = 21
This x value leads to
x+3 = 21+3 = 24
The slower cyclist travels at a speed of 21 km/hr
After 2 hours, s/he travels x*t = 21*2 = 42 km
The faster cyclist travels at a speed of 24 km/hr
After 2 hours, s/he travels (x+3)*t = 24*2 = 48 km
The sum of their distances is 42+48 = 90 km
This confirms our answers.
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Answers:
Slower cyclist speed = 21 km/hr
Faster cyclist speed = 24 km/hr
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! r = rate for first cyclist.
r + 3 = rate for second cyclist.
t = time = 2 hours for both cyclists.
d = distance for first cyclist.
90 - d = distance for second cyclisst.
rate * time = distance formula for first cyclist is r * 2 = d.
rate * time = distance formula for second cyclist is (r + 3) * 2 = 90 - d
simplify the second equation to get:
(r + 3) * 2 = 90 - d becomes:
r * 2 + 6 = 90 - d
subtract 6 from both sides of the equation to get:
r * 2 = 84 - d
solve for d in both equations to get:
d = r * 2 for the first cyclist.
d = 84 - r * 2 for the second cyclist.
subtract the first equaiton from the second to get:
0 = 84 - 2 * r * 2
simplify to get:
0 = 84 - 4 * r
add 4 * r to both sides of the equation to0 get:
4 * r = 84
soolve for r to get:
r = 21
your solution will be:
the rate of the first cyclist is 21 kilometers per hour and the rate of the second cyclist is 24 kilometers per hour.
to confirm:
rate * time = distance for the first cyclist is 21 * 2 = 42.
rate * time = distance for the second cyclist is 24 * 2 = 48.
since they are traveling in opposite directions, then the distance between them will be 90 kilometers after 2 hours have elapsed.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Two cyclists start at the same point and travel in opposite directions.
One cyclist travels 3 km faster than the other.
If the two cyclists are 90 kilometers apart after 2 hours, what is the rate of each cyclist?
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3 km faster -------- 3 km is not speed, it's distance.
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If you mean 3 km/hr faster:
The sum of the speeds is 90/2 = 45
The difference is 3
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r1 + r2 = 45
r1 - r2 = 3
------------------ Add
2r1 = 48
r1 = 24
r2 = 21
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