susan rode her bicycle out into the country for a distance o

susan rode her bicycle out into the country for a distance of 24 miles. on the way back, she took a much shorter route of 12 miles and made return trip in one half hour less time. if her rate out into the country was 4 miles per hour faster than her rate on teh return trip, find both rates.

Solution

D=RT
24=(R+4)T OUT TRIP.
T=24/(R+4) EQ. # 1
12=R(T-.5) RETURN TRIP.
12=RT-.5R
12+.5R=RT
T=(12+.5R)/R EQ # 2
SET THE 2 T EQUATIONS EQUAL & SOLVE FOR R.
24/(R+4)=(12+.5R)/R CROSS MULTIPLY
24R=(R+4)(12+.5R)
24R=12R+48+2R+.5R^2
2R^2+14R+48-24R=0
.5R^2-10R+48=0 MULTIPLY BY 2
R^2-20R+96=0 FACTOR.
(R-12)(R-8)=0
R-12=0
R=12 ANS. T=1.5 ANS
R-8=0
R=8 ANS. T=2 ANS.