Two cyclist leave towns 75moles apart at the same time and travel towards each other. One cyclist travels 7 mph faster than the other. If they meet in 3 hours, what is the rate of each cyclist?

Step-by-step explanation:

Givens

d1 = d

d2 = 75 - d

r1 = x

r2 = x + 7

t = 3

Equation

x*t + (x + 7)*t = 75

This equation represents the total distance travelled. Neither one of the cyclists have gone 75 miles, but they both have gone distances that equal a total of 75 miles.

Solution

3x + (x + 7)*3 = 75

3x + 3x + 21 = 75

6x + 21 = 75

6x = 54

6x/6 = 54/6

x = 9

Answer

The first cyclist is going 9 miles / hr

The second cyclist is going 16 miles / hour

One travels 10.2mph, the other (the one who traveled 7mph faster) traveled at a rate of 14.8mph

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

what is the question here

step-by-step explanation: