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Sagot :
The equation that we need to solve is:
(S + 2*S)*3h = 54mi
The speed of the slower cyclist is 6 mi/h
The speed of the faster cyclist is 12 mi/h.
How to write an equation that models this situation?
Let's define S as the speed of the slower cyclist, thus 2*S will be the speed of the other cyclist.
They travel in opposite directions, and after 3 hours the travel a combined distance of 54 miles, then we can write the equation:
(S + 2*S)*3h = 54mi
With that equation, we can determine the speeds of the cyclists.
Solving for S we get:
(S + 2*S)*3h = 54mi
3*S = 54mi/3h = 18 mi/h
S = (18 mi/h)/3 = 6 mi/h
Then the speed of the slower cyclist is 6 miles per hour, and the speed of the faster cyclist is twice that, so it is 2*6 mi/h = 12 miles per hour.
If you want to learn more about speed:
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