SOLUTION: A man drove 156 km at a constant rate. If he had driven 5km/hr. faster he would made the trip in 12 minutes less time. How fast did he drive? ans. 60 KPH help me with solutio

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A man drove 156 km at a constant rate. If he had driven 5km/hr. faster he would made the trip in 12 minutes less time. How fast did he drive? ans. 60 KPH help me with solutio      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 683843: A man drove 156 km at a constant rate. If he had driven 5km/hr. faster he would made the trip in 12 minutes less time. How fast did he drive?
ans. 60 KPH
help me with solution pls..
Found 2 solutions by josmiceli, lwsshak3:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s+ = his speed in km/hr
+s+%2B+5+ = his speed plus +5+ km/hr
Let +t+ = his time to travel 156 km
+t+-+12%2F60+ his time minus +12+ min
as fraction of an hour
------------------
Equation for actual trip:
(1) +156+=+s%2At+
Equation for 5 km/hr faster:
(2) +156+=+%28+s+%2B+5+%29%2A%28+t+-+1%2F5+%29+
-----------------------------
(2) +156+=+s%2At+%2B+5t+-+%281%2F5%29%2As+-+1+
and
(1) +t+=+156%2Fs+
Substitute (1) into (2)
(2) +156+=+s%2A%28+156%2Fs+%29+%2B+5%2A%28+156%2Fs+%29+-+%281%2F5%29%2As+-+1+
(2) +156+=+156+%2B+780%2Fs++-+%281%2F5%29%2As+-+1+
(2) +0+=+780%2Fs++-+%281%2F5%29%2As+-+1+
(2) +1+=+780%2Fs++-+%281%2F5%29%2As++
Multiply both sides by +5s+
(2) +5s+=+3900+-+s%5E2+
(2) +s%5E2+%2B+5s+-+3900+=+0+
Use quadratic equation:
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-3900+
+s+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A1%2A%28-3900%29+%29%29+%2F+%282%2A1%29+
+s+=+%28-5+%2B-+sqrt%28+25+%2B+15600+%29%29+%2F+2+
+s+=+%28-5+%2B-+sqrt%28+15625+%29%29+%2F+2+
+s+=+%28-5+%2B+125%29+%2F+2+ ( ignore the negative square root )
+s+=+120%2F2+
+s+=+60+
His speed was 60 km/hr
check:
(1) +156+=+60%2At+
(1) +t+=+156%2F60+
(1) +t+=+2.6+
and
(2) +156+=+%28+60+%2B+5+%29%2A%28+2+%2B+3%2F5+-+1%2F5+%29+
(2) +156+=+65%2A%28+2+%2B+2%2F5+%29+
(2) +156+=+130+%2B+26+
(2) +156+=+156+
OK



Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A man drove 156 km at a constant rate. If he had driven 5km/hr. faster he would made the trip in 12 minutes less time. How fast did he drive?
ans. 60 KPH
**
let x=how fast he drove
x+5=speed in 12 min less time
156/x-156/(x+5)=12 min=12/60 hr=0.2 hr
156/x-156/(x+5)=.2
LCD: x(x+5)
156(x+5)+156x=x(x+5)(.2)
156x+780+156x=.2x^2+x
.2x^2+x-780=0
2x+10x-7800=0
x+5x-3900=0
(x+65)(x-60)=0
x+65=0
x=-65(reject, x>0)
or
x-60=0
x=60
how fast he drove=60 km/hr