J, P, and L can each eat ice cream at respective rates of [tex]\dfrac1j,\dfrac1p,\dfrac1\ell[/tex] in gallons of ice cream per hour (gal/hr).
We're given that
[tex]\dfrac1j+\dfrac1p=\dfrac12[/tex]
[tex]\dfrac1p+\dfrac1\ell=\dfrac13[/tex]
[tex]\dfrac1j+\dfrac1p+\dfrac1\ell=1[/tex]
We want to find [tex]\dfrac1j[/tex]. Subtracting the second equation from the third gives
[tex]\left(\dfrac1j+\dfrac1p+\dfrac1\ell\right)-\left(\dfrac1p+\dfrac1\ell\right)=1-\dfrac13[/tex]
[tex]\implies\dfrac1j=\dfrac23[/tex]
so J can eat 2 gallons of ice cream in 3 hours, or 2/3 of a gallon per hour, so that it would take her 3/2 hours, or 1.5 hours, to eat 1 gallon on her own.
Answer:
The given rates are in hours per gallon. If we rewrite them in terms of gallons per hour, we have ...
... Jenny + Penny = 1/2 . . . . gallon per hour
... Penny + Lenny = 3/5 . . . gallon per hour
... Jenny + Penny + Lenny = 1 . . . gallon per hour
Subtracting the 2nd equation from the last, we have ...
... (Jenny +Penny +Lenny) -(Penny +Lenny) = (1) -(3/5)
... Jenny = 2/5 . . . . gallon per hour
It will take Jenny 5/2 = 2.5 hours to eat a gallon of ice cream by herself.
Step-by-step explanation:
