please help math

Question

Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.

Chapter Reference

e

What was the speed of the second cyclist?

Answer 1

two cyclists are 7 miles apart, going in opposite directions

add their speeds together, multiply by time traveled = distance = 7 miles

1st goes 12 mph

2nd goes 12+b mph

distance = rate of speed times time

d= rt

rt=d

(r1+ r2)t = d

(12+b + 12)t = 7

(24+b)t = 7

24t +bt = 7

bt = 7-24t

divide by t

b= 7/t -24 mph

if time =t = 1/4 hr = 15 min, then b = 7/(1/4) -24 = 28-24 = 4 mph

15 minutes = 1/4 hour

the 1st went 12 x 1/4 = 3 miles

the 2nd went 4+12= 16 x 1/4 = 4 miles

the distance between them

after goin in opposite directions

after 15 minutes, at 12 mph & 16 mph

= 3+4 =7 miles