car P travels due East along a straight highway at a constant speed of 30m/s. at 9:00am , P passes Exit 17. At precisely the same moment, car Q passes Exit 16, traveling due West as constant 26m/s. Slightly later, car P and car Q pass the same point. knowing the ecits are exactly 7km apart, how many mintues past 9:00am do the cars pass each other

Question

car P travels due East along a straight highway at a constant speed of 30m/s. at 9:00am , P passes Exit 17. At precisely the same moment, car Q passes Exit 16, traveling due West as constant 26m/s. Slightly later, car P and car Q pass the same point. knowing the ecits are exactly 7km apart, how many mintues past 9:00am do the cars pass each other

Answer 1

It helps to know that Exit 16 is east of Exit 17.

Since the two cars travel 7km in t seconds,

30t + 26t = 7000
t = 125 sec

That would be 2'5"

Answer 2

To find out how many minutes past 9:00 am the cars pass each other, we need to determine the time it takes for them to travel the 7 km between Exit 17 and Exit 16.

First, let's calculate the time it takes for car P to travel the distance between the two exits.

The distance between the exits is 7 km, and car P is traveling at a constant speed of 30 m/s.

Using the formula time = distance / speed, we can calculate the time it takes for car P to travel the distance:

time = distance / speed = 7 km / 30 m/s

Before we proceed, let's convert the distance from kilometers to meters, as the speed is given in meters per second:

7 km * 1000 m/km = 7000 m

Now, let's calculate the time:

time = 7000 m / 30 m/s = 233.33 seconds

Since both cars pass the same point slightly later than their respective exit passages, the time it takes for car Q to reach that point will be slightly less than the time it takes for car P.

The speed of car Q is 26 m/s, and the distance it needs to cover is also 7000 m. Using the same formula:

time = distance / speed = 7000 m / 26 m/s = 269.23 seconds

Now, to find out how many minutes past 9:00 am the cars pass each other, we need to find the difference between the times it takes for car P and car Q:

difference = time (car P) - time (car Q) = 233.33 seconds - 269.23 seconds

To convert the difference to minutes, divide it by 60 (since there are 60 seconds in one minute):

difference (in minutes) = (233.33 seconds - 269.23 seconds) / 60 = -0.6 minutes

Therefore, the cars pass each other around 0.6 minutes before 9:00 am.

Note: The negative sign indicates that the cars pass each other slightly before 9:00 am, which means the actual time will be slightly earlier than 9:00 am.