Travel Time Problem - Please Help?

Question

Two cars start at the same location and travel in the same direction at average speeds of 40 miles per hour and 55 miles per hour. How much time must elapse before the two cars are 10 miles apart?

The answer is 40 minutes .. But how do I get to the answer ?? ..
Can anyone please explain how to solve this problem.

Thank You

Answer 1

55t - 40t = 10
15t = 10
t = 10/15 = 2/3

2/3 of an hour is 40 minutes

Answer 2

Using your formula for distance, we know that d= r*t

1. Let d for car 1 be x, because it traveled some unknown distance. It's distance formula would then be x = 40 * t

2. We know that at the end, the cars were 10 miles a part from each other, so the distance traveled by car 2 in relation to car 1 will be x+10; that means the distance formula for car 2 would be
x+10 = 55 * t

3. As you can see, in each equation, there are two unknowns; x and t for distance traveled and time, respectively. However, we also know that each car traveled the same time over the distance, so we can eliminate the t variable by solving for t in each equation:

For car 1----> x = 40 * t
so ----> t = x/40

For car 2 ----> x+10 = 55t
so ----> t = x+10/55

Again, knowing that the time is the same in both equations, we can now set the two time equations equal to each other to solve for the distance variable x. So:

x/40 = x+10/55

4. Solve the equation algebraically first by multiplying each side by 40 to get x by itself on the left.
x = 40x + 400/55
Then multiply all terms by the 55 in the denominator on the right to remove it.
55x = 40x + 400
15x = 400
x = 26.6666

5. Now that we have a value for x, we can go back to either distance equation and plug it in to find the value for t. I chose to plug it in to the distance equation for car 1 which was
x = 40 * t
26.6666 = 40*t
t = 26.6666/40
t = .6666
So, the time it took for the two cars to travel until they were 10 miles apart from each other is .6666 hours

***Remember the terms are in miles per hour. Your answer is given in minutes, so the final step is to convert .6666 hours to minutes****

6. Convert hours to minutes:
Minutes = .6666 hrs *60 minutes/1 hr
Minutes = .6666 * 60 (the hrs cancel each other out)
Minutes = 39.99 which can be rounded to

40 minutes

I hope this explains.

Answer 3

Basically, this is how you get the 40 minutes:

10/15 * 60

The explanation is this:

After 1 hour (60 minutes) they are 15 miles apart, because the first car has gone 40 miles and the second has gone 55 miles.

Thus, if they are 15 miles apart at 60 minutes, then they are 10 miles apart at 10/15 * 60 minutes = 40 minutes.

~ ♥ ~

Answer 4

Set up two equations
for the first car
speed * time = x miles
40 mph *t = x (1)
for the second car
55 mph * t = x + 10
therefore
55 *x\40 = x + 10
55x = 40x + 400
x = 26.67 miles
sub into (1)
40 mph * t = x
t = 26.67 / 40
t = .667 hours ( two thirds)
t = 40 minutes