Algebra one, speed

Question

The bicyclists were 300 miles apart at 3 p.m. and were headed toward each other. If they met at 9 p.m. and one was traveling 20 miles faster than the other, what was the speed of each bicyclist.

Answer 1

300 miles in 6 hours

F = 20+S = Faster speed

300/6 = 50/2 = 25 mph average speed

S+20+S = 2S +20 = 50= combined speed

2S = 30

S =30/2 = 15 mph = Slower guy's speed

F = 15+20 = 35 mph = Faster guy's speed

Answer 2

Distance = rate x time.

Both travel for 6 hrs (3pm to 9 pm) before meeting.

1st bike at x mph; 2nd bike at (x + 20) mph

Equation for distance is 6x + 6(x + 20) = 300

6x + 6x + 120 = 300

12x = 180

x = 15 mph ; x + 20 = 35 mph

Check: 6(15) = 90 mi for 1st bike; 6(35) = 210 mi for 2nd bike. Total 300 mi.