Finding the rate of speed

Question

richard bicycles a total of 135 miles in 8 hours on saturday and sunday while training for a race. On saturday he rode for 75 miles. on sunday he increased his speed from saturday by 5mph. Find his speed for each day

Answer 1

 

 So 75 miles on Saturday and 60 miles on Sunday

 

 75 = R*(8-t) = 8r - rt

 

 60 = (R+5)* t = rt + 5t

 

135 = 8r + 5t

 

(135 - 5t)/8 = r

 

 

75 = (135-5t)/8 *(8-t)  <---- distance = rate x time

 

600 = (135 - 5t)*(8-t)

 

600 = 1080 - 40t - 135t + 5t^2

 

600 = 1080 - 175t + 5t^2

 

0 = 5t^2 - 175t + 480

 

0 = t^2 - 35t + 96

 

0 = (t - 3)(t-32)

 

t-32=0 results in negative times

 

t-3=0 ---> t = 3 ---> r = (135 - 5*3)/8 = (135-15)/8 = 120/8 = 60/4 = 15

 

 So  5 hours x 15 mph = 75 miles  and 3 hours at 20 mph = 60 miles