word problem help

Question

A trained me to trip of 600 miles between two cities. If it had averaged 10 mph more it would've required two hours less to make the trip. Find the rate of speed of the train

Answer 1

d=rt

600=rt

600=(r+10)(t-2)

from 600=rt we get 600/r=t

substitute

600=(r+10)([600/r]-2)

multiply both sides by r

600r=r(r+10)([600/r]-2)

600r=(r²+10r)([600/r]-2)

use FOIL on the right side

600r=600r+6000-2r²-20r

subtract 600r from both sides

0=6000-2r²-20r

2r²+20r-6000=0

r²+10r-3000=0

3000=3*2*2*2*5*5*5=(3*2*2*5)*(2*5*5)=60*50 and 60-50=10, the coefficient of the middle term

factor

(r+60)(r-50)=0

r-50=0

r=50 mph is the speed of the train

Answer 2

Speed = Distance /Time taken

 

Average speed = Total distance /total time taken

Let T be time taken in first case

 

V=600/T

 

In second case

 

 V+10 = 600/ (T-2)

substituting T =600/V

V+10 = 600V / (600-2V)

 

(V+10).(600-2V) =600V

 

V² +10V -3000=0   Gives  V= 50 miles/hr  Ans