two buses leave at the same time.
one travels west at 40 mph.
the other goes north at 30 mph.
When will they be 400 miles apart?
(30t)^2 + (40t)^2 = 400^2
30t+40t=400
70t=400
t= 400/70
=5.71hrs
After 5.71hrs they will be at 400miles apart.
Deez N***
To find out when the two buses will be 400 miles apart, we can use the concept of distance and time.
Since one bus is traveling west and the other is going north, they are moving at right angles to each other, which forms a right triangle. The distance between the two buses is the hypotenuse of this right triangle.
Let's denote the time it takes for the buses to be 400 miles apart as "t" hours.
For the bus traveling west at 40 mph, the distance it covers in "t" hours is given by the formula: Distance = Speed × Time. So, the distance traveled by this bus is 40t miles.
Similarly, for the bus going north at 30 mph, the distance it covers in "t" hours is also given by: Distance = Speed × Time. So, the distance traveled by this bus is 30t miles.
Now, using the Pythagorean theorem, we can find the distance between the two buses:
Distance^2 = (40t)^2 + (30t)^2
Substituting the values:
400^2 = (40t)^2 + (30t)^2
Simplifying the equation:
160,000 = 1,600t^2 + 900t^2
160,000 = 2,500t^2
Dividing both sides by 2,500:
64 = t^2
Taking the square root of both sides:
t = √64
t = 8
Therefore, the two buses will be 400 miles apart after 8 hours.