SOLUTION: Hello ... I need help on my homework ... please help me. A bus and a car left a place at the same time travelling in opposite direction. After 2 hours, the distance between them is

Question 904435: Hello ... I need help on my homework ... please help me. A bus and a car left a place at the same time travelling in opposite direction. After 2 hours, the distance between them is at most 350 km. What is the mathematical statement that represents the distance between the two vehicles after 2 hours?
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
rate * time =distance
here we have
rate * time +rate * time =distance
where x and y are the cars speed.
2*x+2*y=350
or
2*(x+y)=350

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it's not clear whether the two vehicles are traveling at the same speed or not.

the equation will be different depending on that fact.

assuming they are both traveling at the same speed, then you get the following equation.

let a equal the speed of each of the cars.

rate * time = distance.

since they are traveling in opposite directions, they are working together to increase the distance between them.

the equation of r * t = d becomes (a + a)*t = d

this can be simplified to 2*a*t = d

since t = 2 hours and d will be less than or equal to 350 miles, the equation becomes 2*a*2 <= 350 which becomes 4*a <= 350.

here you can solve for a to get a <= 350/4 which makes a <= 87.5

when a is equal to 87.5, they will be 350 miles apart in 2 hours.

one of the vehicles is traveling east at 87.5 miles per hour for 2 hours which makes that vehicle travel 175 miles.

the other vehicle is traveling west at 87.5 miles per hour for 2 hours which makes that vehicle travel 175 miles.

175 * 2 = 350.

in 2 hours the vehicles are 350 miles apart.

if a is less than 87.5, then they will be less than 350 miles apart.
if a is more than 87.5, then they will be more than 350 miles apart.

when the speeds are different, you can't solve for one speed only.

the equation becomes 2*(a + b) <= 350 which can be simplified to 2a + 2b <= 350 miles.

you can solve for a in terms of b or you can solve for b in terms of a.

I'll solve for a in terms of b and i will get a <= (350 - 2b) / 2 which can be simplified to a <= 175 - b

you would then have to assume a speed for b which is less than 175 miles per hour and a will be defined from that.

assuming b travels at 100 miles per hour, then a has to travel less than or equal to 75 miles per hour.

assume a travels at 75 miles per hour and b travels at 100 miles per hour, then you get the following:

2*75 = 150 miles for one car.
2*100 = 200 miles for the second car.
together they travel a total of 350 miles.

you can still solve the problem but you have to assume a value for one of them because the equation has 2 variable which can't be solved except in terms of one or the other.

in this case, you can get an infinite number of solutions depending on what you assume the value of b is.

sorry for the complexity, but you didn't specify whether both cares were traveling at the same speed or not.

if they were, then the problem is much simpler as shown when I assumed the speeds were the same.

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