A car leaves Tower City and travels 600 mi.The return trip is made at a speed that is 10mph faster. Total time for the round trip is 22 hr.

Question

can you find the speed on each part of the trip.

Answer 1

distance=rate*time

600=rt

600=(r+10)(22-t)

600=22r+220-rt-10t

from the first equation 600=rt, 600/r=t

substitute

600=(22r+220-r(600/r)-10(600/r))

600=22r+220-600-(6000/r)

600=22r-380-(6000/r)

multiply both sides by r

600r=22r²-380r-6000

22r²-380r-600r-6000=0

22r²-980r-6000=0

divide by 2

11r²-490r-3000=0

11*3000=11*3*2*2*2*5*5*5=(11*2*5*5)*(3*2*2*5)=550*60 and 550-60=490

factor

(11r   )(r   50) so far...

(11r+60)(r-50)=0

r-50=0

r=50 mph

r+10=60 mph

check:600=50t, t=12 hours

600=60*(22-12), 600=60*10=600

actually, using the quadratic equation is easier to find r because √372,100=610, a perfect square