Question 1056463
Let the younger sister's time=x
the older sister's time is x+10
in 1 minute, the younger sister does 1/x of the car and the older sister does 1/(x+10) of the car.
in 24 minutes, they do the whole car together.
Therefore 24/x+24/(x+10)=1 (the whole car)
Multiply by x(x+10) both sides to clear fractions
24(x+10)+24x=x^2+10x, which is x(x+10)
x^2+10x=24x+240+24x
x^2-38x-240=0
x=(1/2)(38+/-sqrt(38^2+960); sqrt term is of (2404)=49.03
Therefore, the one positive root is (1/2)87.03=43.52 min
43.5 min for the younger sister ANSWER
53.5 min for the older sister
(24/43.5)=0.55
(24/53.5)=0.45