Applications Involving Rational Expressions

Question

Jessica drove 490 miles to her parents house. On her way there her average speed was 24 miles per hour faster than on her way home. If she spent a total of 14 hours driving, find the two rates.

Answer 1

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!