# Thread: Solving Problems with Rational Expressions

1. ## Solving Problems with Rational Expressions

This is my first time here, i really hope that i am in the right section. I have having alot of problems with problem solving, i am in solving problems with rational expressions

This is the question that i have:

Gloria drives a distance of 90 km in 30 min less time than Jayden drives the same distance. What is the speed of each driver if Gloria drives 1.5 times fast than Jayden.

I need to first write an equation for this and then solve. How can i do this?

2. Distance = Rate x Time

in this case the distance is the same for both so set
$\displaystyle R_GT_G = R_JT_J$

3. Originally Posted by nuckers
This is my first time here, i really hope that i am in the right section. I have having alot of problems with problem solving, i am in solving problems with rational expressions

This is the question that i have:

Gloria drives a distance of 90 km in 30 min less time than Jayden drives the same distance. What is the speed of each driver if Gloria drives 1.5 times fast than Jayden.

I need to first write an equation for this and then solve. How can i do this?
From d = vt:

Jayden: $\displaystyle 90 = vt$ .... (1)

Gloria: $\displaystyle 90 = \frac{3}{2} v \left(t - \frac{1}{2}\right)$ .... (2)

Your job is to solve equations (1) and (2) simultaneously for $\displaystyle v$. I suggest solving for $\displaystyle t$ first ....

4. Originally Posted by nuckers
This is my first time here, i really hope that i am in the right section. I have having alot of problems with problem solving, i am in solving problems with rational expressions

This is the question that i have:

Gloria drives a distance of 90 km in 30 min less time than Jayden drives the same distance. What is the speed of each driver if Gloria drives 1.5 times fast than Jayden.

I need to first write an equation for this and then solve. How can i do this?
Let the time it takes Gloria to drive the 90km be $\displaystyle t$, where $\displaystyle t$ is measured in mins.

Therefore, the time it takes Jayden is $\displaystyle t + 30$.

Let $\displaystyle G$ represent Gloria's speed, and $\displaystyle J$ represent Jayden's speed.

Therefore $\displaystyle G = \frac{90}{t}$ and $\displaystyle J = \frac{90}{t + 30}$.

We also know that Gloria's speed is 1.5 times faster than Jayden's.

So $\displaystyle G = \frac{3}{2}J$

$\displaystyle \frac{90}{t} = \frac{3}{2}\left(\frac{90}{t + 30}\right)$

$\displaystyle \frac{90}{t} = \frac{135}{t + 30}$

$\displaystyle \frac{t}{90} = \frac{t + 30}{135}$

$\displaystyle 135t = 90(t + 30)$

$\displaystyle 135t = 90t + 2700$

$\displaystyle 45t = 2700$

$\displaystyle t = 60$.

So it takes Gloria 60 mins, and Jayden $\displaystyle 60 + 30 = 90$ mins.

5. thank you for all your help everyone

6. ## Note on units.

Note: The solution in post #3 will give time in hours and speed in km/hr. The solution in post #4 will give time in minutes and speed in km/min.