<PRE><B>Question 975882</B>
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

{{{288/s}}} - {{{288/(s+8)}}} = .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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