<PRE><B>Question 736876</B>
 John drives along a straight motorway at a constant speed for 120km.
 Next day he completes the same journey travelling 10km/h faster.
 He completes this journey in 10 mins less than the first journey.
 find the 2 speeds at which he travelled. 
:
let s = his first speed
then
(s+10) = his faster speed
:
change 10 min to 1/6 hr
:
Write a time equation, time = dist/speed:
:
{{{120/s}}} - {{{120/((s+10))}}} = {{{1/6}}}
multiply by 6s(s+10) to clear the denominators, resulting in:
6(s+10)*120 - 6s(120) = s(s+10)
120(6s+60) - 720s = s^2 + 10s
720s + 7200 - 720s = s^2 + 10s
a quadratic equation
0 = s^2 + 10s - 7200 = 0
Factors to
(s+90)(s-80) = 0
the positive solution all we want here
s = 80 km/hr and 90 km/hr are the two speeds
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