Question 1189896
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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
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