SOLUTION: A car takes 2 hours less for a journey of 300km, if its speed is increased by 5 km/h from its usual speed. Find its usual speed.

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Question 230078: A car takes 2 hours less for a journey of 300km, if its speed is increased by 5 km/h from its usual speed. Find its usual speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = it's usual speed
Let t = it's usual time for 300 km journey
given:
(1) 300+=+st km
(2) 300+=+%28s+%2B+5%29%2A%28t+-+2%29
-------------------------
This is 2 equations and 2 unknowns, so it's solvable
Expand (2)
(2) 300+=+%28s+%2B+5%29%2A%28t+-+2%29
(2) 300+=+st+%2B+5t+-+2s+-+10
substitute (1) in (2)
300+=+300+%2B+5t+-+2s+-+10
5t+=+2s+%2B+10
t+=+%282%2F5%29%2As+%2B+2
Plug this back into (1)
(1) 300+=+st
300+=+s%2A%28%282%2F5%29%2As+%2B+2%29
300+=+%282%2F5%29%2As%5E2+%2B+2s
1500+=+2s%5E2+%2B+10s
2s%5E2+%2B+10s+-+1500+=+0
s%5E2+%2B+5s+-+750+=+0
Solve using quadratic formula
s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+5
c+=+-750
s+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-750%29+%29%29%2F%282%2A1%29+
x+=+%28-5+%2B-+sqrt%28+25+%2B+3000+%29%29%2F2+
s+=+%28-5+%2B-+sqrt%28+3025+%29%29%2F2+
s+=+%28-5+%2B-+55%29%2F2+
s+=+25 (the negative answer can't be used)
It's usual speed is 25 km/hr
check answer:
(1) 300+=+st km
300+=+25t
t+=+12 hrs
(2) 300+=+%28s+%2B+5%29%2A%28t+-+2%29
300+=+%2825+%2B+5%29%2A%2812+-+2%29
300+=+30%2A10
300+=+300
OK