SOLUTION: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express       Log On


   

Question 550389: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express train in km/hr.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = speed of express train
+s+-+12+ = speed of slower train
Let +t+ = time for express train to cover +240+ km
------------
Express train:
(1) +240+=+s%2At+
Slower train:
(2) +240+=+%28+s+-+12+%29%2A%28+t+%2B+1+%29+
-------------------------
(2) +240+=+s%2At+-+12t+%2B+s+-+12+
Substitute (1) into (2)
(2) +s%2At+=+s%2At+-+12t+%2B+s+-+12+
(2) +12t+=+s+-+12+
(2) +t+=+%281%2F12%29%2As+-+1+
Substitute this into (1)
(1) +240+=+s%2A%28+%281%2F12%29%2As+-+1+%29+
(1) +240+=+%281%2F12%29%2As%5E2+-+s+
(1) +2880+=+s%5E2+-+12s+
(1) +s%5E2+-+12s+=+2880+
Complete the square
(1) +s%5E2+-+12s+%2B+%2812%2F2%29%5E2+=+2880+%2B+%2812%2F2%29%5E2+
(1) +s%5E2+-+12s+%2B+36+=+2880+%2B+36+
(1) +%28+s+-+6+%29%5E2+=+2916+
(1) +%28+s+-+6+%29%5E2+=+54%5E2+
(1) +s+-+6+=+54+
(1) +s+=+60+
The speed of the express train is 60 km/hr
check answer:
(1) +240+=+s%2At+
(1) +240+=+60t+
(1) +t+=+4+ hrs
and
(2) +240+=+%28+60+-+12+%29%2A%28+t+%2B+1+%29+
(2) +240+=+48%2A%28+t+%2B+1+%29+
(2) +240+=+48t+%2B+48+
(2) +48t+=+192+
(2) +t+=+4+ hrs
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
n express train makes a run of 240 km at acertain speed.
Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance.
find the speed of the express train in km/hr.
:
let s = speed of the express
then
(s-12) = speed of the other train
:
Write a time equation, time = dist/speed
:
Other train time - Express train time = 1 hr
240%2F%28%28s-12%29%29 - 240%2Fs = 1
Multiply by s(s-12)
s(s-12)*240%2F%28%28s-12%29%29 - s(s-12)*240%2Fs = s(s-12)
Cancel the denominators and you have
240s - 240(s-12) = s^2 - 12s
:
240s - 240s + 2880 = s^2 - 12s
combine like terms and arrange as a quadratic equation
0 = s^2 - 12s - 2880
you can use the quadratic equation but this will factor to
(s+48)(s-60) = 0
s = 60 km/hr is the the express train
:
:
check this by finding the times of each
240/48 = 5 hrs
240/60 = 4 hrs