On a 135-mile bicycle excursion, Maria averaged 5 miles per hour slower during the

  • Thread starter Thread starter jamie s
  • Start date Start date
J

jamie s

Guest
last 75 miles than for the ? On a 135-mile bicycle excursion, Maria averaged 5 miles per hour slower during the last 75
miles than for the first 60 miles. The entire trip took 8 hours. Find her rate for the first 60
miles.
__________________________________________________________________
 
D = rt

For first 60 miles:
60 = rt

For last 75 miles:
75 = (r - 5)(8 - t)

t = 60/r

75 = (r - 5)(8 - 60/r)

75 = 8r - 60 - 40 + 300/r

75r = 8r^2 - 100r + 300

8r^2 - 175r + 300 = 0

a = 8
b = -175
c = 300

r = (175 +/- sqrt((-175)^2 - 4(8)(300)))/2(8)

r = (175 +/- sqrt(30625 - 9600))/16

r = (175 +/- sqrt(21025))/16

r = (175 +/- 145)/16

r = 30/16 or 320/16

r = 15/8 or 20

Let's check these answers:
t = 60/(15/8) or 60/20
t = 32 or 3

t cannot = 32, so t = 3 and r = 20

So, Maria's rate for the first 60 miles is:
20 mph
 
Back
Top