How is inductive reasoning used to recognize mathematical relationships?

A general way of explaining this is

Suppose that we have a given property (or a pattern if we are working with a series of numbers):

Now, if that property is true, for example, for the numbers 1, 2, 3... etc.  Then we can suppose that the property is also true for an unknown number N.

Now, if using the hypothesis that the property is true for N, we can prove that the property is also true for N + 1, then we actually proved that the property is true for all the set.

We actually can use any set, not only the natural numbers.

For example, we can use the set of the even numbers {2, 4, 6, 8}, suppose that the property is true for a random number N, that is even, and then see if using that hypothesis we can prove that the property is also true for the next number in the set; N + 2.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.