Distance, speed (rate) and time are related by the formula d=rt
On her trip to her parents' house, you have
490 = (r+24) * t1
On the way back,
490 = r * t2
The total time was 14 hours. If you solve each equation above for t and add, you get
490/(r+24) + 490/r = 14
Generally, the easiest way to solve a rational equation like this is to multiply everything by the common denominator, which will leave you with a quadratic equation that you can solve by factoring or the quadratic formula.
Here, the LCD is r(r+24). Multiplying through:
r(r+24)*490/(r+24) + r(r+24)*490/r = r(r+24)*14
The denominators all cancel, you can distribute and then collect all your terms on one side to solve. I'll leave that up to you.
I hope this helps, and if you have further questions, please comment!