SOLUTION: a traine cover 288 km at constant speed.If its speed was 8kmps more it would have taken 24 minutes less to travel the distance.Find the speed of the train.(in km)?

Question 975882: a traine cover 288 km at constant speed.If its speed was 8kmps more it would have taken 24 minutes less to travel the distance.Find the speed of the train.(in km)?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a train covers 288 km at a constant speed.
If its speed was 8 kmps more it would have taken 24 minutes less to travel the distance.
Find the speed of the train.(in km/hr)?
:
let s = the speed of the train
then
(s+8 ) = the faster speed
:
Change 24 min to hrs: 24/60 = .4 hrs
:
Write a time equation: time = dist/speed
:
Actual speed time - faster speed time = .4 hrs
- = .4
multiply equation by s(s+8), cancel the denominators:
288(s+8) - 288s = .4s(s+8)
288s + 2304 - 288s = .4s^2 + 3.2s
A quadratic equation
0 = .4s^2 + 3.2s - 2304
Use the quadratic formula to find s, a=.4; b= 3.2; c=-2304
I got a positive solution of
s = 72.0 km/hr
:
:
Confirm this by finding the actual time at each speed.
288/72 = 4.0 hrs
288/80 = 3.6 hrs (8 km/hr faster)
-----------------------
time difference: .4 hrs which is 24 min

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