Question

Two cyclists, 55 miles apart, start riding toward each other at the same time. One cycles 5 miles per hour faster than the other, and they meet after 5 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?

Answer 1

Answer:

r = 6 mph and f = 11 mph

Step-by-step explanation:

Representations:  

1) speed of faster cyclist:  f = r + 5

2) speed of slower cyclist:  r

Distances covered:

(r + 5)(5 hr) + r(5) = 55 mi (total distance covered)

Then 5r + 25 + 5r = 55, or, after reducing this equation:

r + 5 + r = 11, or

2r = 6

Then r = 6 mph and f = 11 mph