# Math Help - Uniform motion & Inequalities

1. ## Uniform motion & Inequalities

Hi I have 3 questions I've been working to try and figure these out with no luck.

1) A plane can fly 1050 miles in the same time as it takes a car to go 280 miles. If the car travels 110 mph slower than the plane, find the speed of the plane.
Using ${r}$ as your variable to represent the speed of the plane in miles per hour, write an equation using the information above that can be solved to find the answer to this problem.

i figure D=r*t => you know distance and r of the car is r-110, can i assume a value for time or something else?

2) Sarah can run 80 yards in 15 seconds. Wendy can run the same distance in 20 seconds. If Wendy is 25 yards ahead of Sarah when they both start running, how long does it take for Sarah to catch Wendy? Write an equation that using the variable ${t}$ to represent the time it takes for Sarah to catch Wendy.

Again D=r*t => sarah runs at a rate of 5.333 m/sec and wendy at a rate of 4 m/sec. D=distance sarah has to run to catch wendy and D-25= distance wendy has to run until sarah catches her.

3) $\frac{{x}}{{3}}\lt{19}+\frac{{{2}{x}-{5}}}{{6}}$
im just lost here.. i considered taking the left side *2 to make the denominators the same then subtracting the (2x-5)/6 from both sides or something along those lines.. but that doesn't seem like it works...

Thanks for any help

2. Originally Posted by xsavethesporksx
Hi I have 3 questions I've been working to try and figure these out with no luck.

1) A plane can fly 1050 miles in the same time as it takes a car to go 280 miles. If the car travels 110 mph slower than the plane, find the speed of the plane.
Using ${r}$ as your variable to represent the speed of the plane in miles per hour, write an equation using the information above that can be solved to find the answer to this problem.

i figure D=r*t => you know distance and r of the car is r-110, can i assume a value for time or something else?
Hi

Let $r_c$ be the speed of the car
You know that for a certain (unknown) time T

$r \times T = 1050$

$r_c \times T = 280$

Dividing these two equations will give you an additional equation with respect to $r_c = r - 110$