Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny trav
els 10 miles per hour faster than Maureen. (Hint: speed=distance/time) Jenny's speed is ______ miles per hour.
Maureen's speed is _____ miles per hour.
Make chart (rate=speed) distance=time times rate D=TR T=D/R R=D/T D T R J 60 x-2 y+10 M 50 x y
xy=50 (x-2)(y+10)=60 solve for x and y xy=50 divde both sides by x y=50/x subsitute (x-2)(50/x+10)=60 distribute 50x/x-100/x+10x-20=60 50-100/x+10x-20=60 add like terms 10x-100/x+30=60 10x^2/x-100/x+30=60 (10x^2-100)/x+30=60 subtract 60 from both sides (10x^2-100)/x-30=0 add 30 to both sides (10x^2-100)/x=30 multiply both sides by x
10x^2-100=30x subtract 30x from both sides 10x^2-30x-100=0 factor out the 10 (10)(x^2-3x-10)=0 if you have xy=0 then x and/or y=0 so 10≠0 so (x^2-3x-10)=0 factor by finding what 2 numbers multiply to get -10 and add to get -3 the numbers are -5 and 2 so (x^2-3x-10)=(x-5)(x+2)=0 so x-5=0 x+2=0
x-5=0 add 5 to both sides x=5
x+2=0 subtract 2 from both sides x=-2 false since time cannot be negative
x=5 x times y=50 x=5 5 times y=50 divid eby 5 y=10=Maureen's speed y+10=10+10=20=Jenny's speed
Jenny's speed is <u>20</u> miles per hour Maureen's speed is <u>10</u> miles per hour
