Solving Problems with Rational Expressions

**nuckers** · January 4th 2010, 05:50 PM

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?

**bigwave** · January 4th 2010, 06:03 PM

Distance = Rate x Time

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

**mr fantastic** · January 4th 2010, 06:09 PM

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: $90 = vt$ .... (1)

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

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

**Prove It** · January 4th 2010, 06:10 PM

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 $t$ , where $t$ is measured in mins.

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

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

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

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

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

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

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

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

$135t = 90(t + 30)$

$135t = 90t + 2700$

$45t = 2700$

$t = 60$ .

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

**nuckers** · January 4th 2010, 06:19 PM

thank you for all your help everyone

**mr fantastic** · January 4th 2010, 06:21 PM

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.

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