Two bicyclists ride in opposite directions. The speed of the second bicyclist is 5 miles per hour faster than the first. After 2 hours they are 70 miles apart. Find their rates. A. 15 mi/h; 20 mi/h B. 32.5 mi/h; 37.5 mi/h C. 20 mi/h; 25 mi/h

A. 15 mi/h; 20 mi/hr

Explanation:

Let y mi/h be the speed of first bicyclist. According to the problem, (y + 5) mi/h be the speed of second bicyclist.

After 2 hours,

Distance covered by first bicyclist, d₁ = 2y

Distance covered by second bicyclist, d₂ = 2 (y+5)

Since, the two bicyclist are moving in opposite directions. Thus sum of their

distance is equal to the total distance they are apart, that is,

d₁ + d₂ = 70

2y + 2 (y+5) = 70

4y + 10 = 70

4y = 60

y = 60/4 = 15 mi/h

Speed of first bicyclist = y = 15 mi/h

Speed of second bicyclist = y + 5 = 15 + 5 = 20 mi/h