At 10: 00 a. m. two boys start out on their bikes to meet each other from towns located 68 miles apart. at 1: 00 p. m. they meet. if one boy traveled 3 miles per hour faster than the other, what was the rate of speed of each boy?

The rate of each boys are as follows:

The boy at slower speed = 9.8 mph (slow speed)

The boy at faster speed= 12.8 mph (faster speed)

Speed can be defined as the distance covered per unit time. That is, speed = distance/time.

Since the faster boy travels 3 miles per hour faster than the other, therefore

slower speed= x and

faster speed= x + 3

The total time for each boy = 3 hours

To find out the distance for each boy, you must multiply the 3 hours (time) and speed together.

so distance = time*speed

Therefore,

slower distance = 3x

faster distance = 3(x +3)

Then you can add them together to get the total distance.

To Solve for slow speed(x).

3x + 3(x + 3) = 68

3x + 3x + 3×3 = 68

6x + 9 = 68 add like terms

6x = 68 - 9

6x = 59

x = 59/6 = 9.8 mph (slow speed)

Therefore, faster speed,

x + 3 = 12.8 mph (faster speed)

Therefore, the rate of each boys are 9.8 mph (slow speed) and 12.8 mph (faster speed).

Learn more about speed here:

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)