Two buses leave the same station at 8:00 pm. One bus travels north at the rate of 30 kph and the other travels east at 40 kph. How many kilometers apart are the buses at 10 pm?
think of a scaled-up 3-4-5 right triangle.
100km
To find the distance between the two buses at 10 pm, we need to calculate the distance each bus has traveled during that time.
Let's start with the bus traveling north. It travels at a rate of 30 kph and has been traveling for 2 hours (from 8 pm to 10 pm). So, the distance traveled by the northbound bus is:
Distance = Speed x Time
Distance = 30 kph x 2 hours
Distance = 60 km
Now, let's consider the bus traveling east. It travels at a rate of 40 kph and has also been traveling for 2 hours. So, the distance traveled by the eastbound bus is:
Distance = Speed x Time
Distance = 40 kph x 2 hours
Distance = 80 km
Now, we can use the Pythagorean theorem to find the distance between the two buses. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, the distance between the two buses is:
Distance = √(Distance north^2 + Distance east^2)
Distance = √(60^2 + 80^2)
Distance = √(3600 + 6400)
Distance = √10000
Distance = 100 km
Therefore, the two buses are 100 kilometers apart at 10 pm.
To find the distance between the two buses at 10:00 pm, we need to consider their respective speeds and the time elapsed.
First, let's calculate the time difference between 8:00 pm and 10:00 pm: 10:00 pm - 8:00 pm = 2 hours.
Now, let's consider the motion of each bus separately:
- The northbound bus travels at a speed of 30 kph for 2 hours, covering a distance of 30 kph × 2 hours = 60 kilometers.
- The eastbound bus travels at a speed of 40 kph for 2 hours, covering a distance of 40 kph × 2 hours = 80 kilometers.
To find how far apart the two buses are, we can use the Pythagorean theorem, since the two distances form the legs of a right triangle. The distance between the buses is given by the formula:
Distance = √((Northbound distance)^2 + (Eastbound distance)^2)
Plugging in the values we calculated:
Distance = √(60^2 + 80^2) = √(3600 + 6400) = √10000 = 100 kilometers.
Therefore, the two buses are 100 kilometers apart at 10:00 pm.