Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 mph. Find r. His original speed was r = mph.

Given Information:

Distance = 160 miles

Required Information:

Rate = r = ?

Rate = r = 20 mph

Step-by-step explanation:

Recall that the rate is given by

Rate = distance/time

It is given that the same trip would have taken 2 hours longer if he had decreased his speed by 4 mph.

Mathematically,

Simplify the equation

Now we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method  

So,

OR

Since rate cannot be negative, discard the negative value of r

Therefore, the rate is

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