Two cyclists, 96 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other, and they meet after 4 hours of riding. a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists?

r = rate of slower cyclist

3r = rate of faster cyclist

distance covered by slower cyclist = 4r  (rate*time)

distance covered by faster cyclist = 12r  

total distance = 96

4r + 12r = 96

r = 6

3r = 18 (faster cyclist rate is 18 mph)

Step-by-step explanation:

.

5+2x=a

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step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15