You and your friend part at an intersection. You drive off north at a constant speed, and your friend drives east at a speed that is 10 mph higher. After 4 hours the distance between you and your friend is 368.78 miles. You have been driving at mph. (Round to the nearest mile).
Who is it, Michael or Emma ?
http://www.jiskha.com/display.cgi?id=1441674868
My Name is Michael Emmanuel
To find the speed at which you are driving, we need to use the distance formula and the information given.
Let's say your speed is x mph. Your friend, who is driving east, has a speed that is 10 mph higher than yours, so their speed would be (x + 10) mph.
Since you have been driving north for 4 hours, the distance you have traveled can be calculated by multiplying your speed (x mph) by the time (4 hours):
Distance traveled by you = x mph * 4 hours = 4x miles
Similarly, your friend has been driving east for 4 hours, so the distance they have traveled can be calculated by multiplying their speed (x + 10 mph) by the time (4 hours):
Distance traveled by your friend = (x + 10) mph * 4 hours = 4(x + 10) miles
Now, we have two sides of a right-angled triangle formed by you, your friend, and the distance between you. The distance between you and your friend is the hypotenuse of the triangle, which is given as 368.78 miles.
Using the Pythagorean theorem, we can find the equation for the distance between you and your friend:
Distance between you and your friend = √((Distance traveled by you)^2 + (Distance traveled by your friend)^2)
Substituting the calculated distances, we have:
368.78 = √((4x)^2 + (4(x + 10))^2)
Squaring both sides of the equation, we get:
(368.78)^2 = (4x)^2 + (4(x + 10))^2
Now, we can solve this quadratic equation for x.
(368.78)^2 = 16x^2 + 16(x^2 + 20x + 100)
Simplifying further:
(368.78)^2 = 16x^2 + 16x^2 + 320x + 1600
(368.78)^2 = 32x^2 + 320x + 1600
Let's simplify by dividing both sides by 32:
(368.78)^2 / 32 = x^2 + 10x + 50
Simplifying:
(x^2 + 10x + 50) = (368.78)^2 / 32
Now, we can solve this quadratic equation for x. Plugging the equation into a quadratic formula calculator or using factoring techniques can help determine the value of x, which represents your speed.