Solving distance, rate, and time using a set of linear equations

Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels
7

/kmh
faster than the other. If the two cyclists are
255km
apart after
5
hours, what is the rate of each cyclist?

Answer 1

Suppose the rate of the slower cyclist is X km/h, because another cyclist (the faster one) travels 7 km/h faster than the other (the slower cyclist), therefore, the rate of the faster cyclist is (X + 7) km/h. 

 

Both of them traveled 5 hours, so the distance of the slower cyclist traveled is 5 X km, the distance of the faster cyclist traveled is 5(X + 7) km. Remember: Distance = Rate x Time.

 

Because they started at the same point and traveled in opposite directions, after 5 hours, they are apart 255 km, so, it means, the total distance they traveled is 255 km.

 

And then we set up the equation, it would be:

 

5 X + 5 (X + 7) = 255

5 X + 5 X + 35 = 255 (distributive property)

10 X = 220 (combination and subtraction)

X = 22(km/h) (division)

 

X + 7 = 29(km/h)

 

The rate of the slower cyclist is 22 km/h, and the rate of the faster cyclist is 29 km/h.