There are many ways of doing math in Algebra, but the one way which works the best for me is by using multiple steps and by writing equations.

Equations are very important to have, for without them, it is quite impossible to get problems right, for example:

Juarez's speed was 4 times as great as that of Benito. Thus, Juarez could travel 1440 miles in only 4 hours more than it took Benito to travel 120 miles. Find the speed of both and the times of both.

So in this example there are multiple equations to write:

rate(J) * time(J) = 1440 miles Rate * Time = Distance

rate(B) * time(B) = 120 miles Rate * Time = Distance

rate(J) = 4 * rate(B) Rate of Juarez is 4 times the rate of Benito

time(J) = time(B) + 4 Time of Juarez is 4 hours longer than Benito

So by this question we got four equations, and now what we want to do, is to substitute the rate and time of Juarez into the first equation like so:

rate(J) = 4 * rate(B) goes into the rate(J) which was in the first equation so it now is:

4 * rate(B) * time(J) = 1440 Rate of Juarez substituted

And now we substitute the time of Juarez for the time of Benito + 4 :

4rate(B) * [time(B) + 4] = 1440

4rate(B) * time(B) + 16rate(B) = 1440 Multiply...

4(120) + 16rate(B) = 1440 Now substituted with equation 2...

16rate(B) = 1440 - 480 Brought 480 over...

16rate(B) = 960 Subtracted...

rate(B) = 60 Divided!

After finding the rate of Benito we find the rest by using the four equations we got in the beginning:

rate(J) = 4(60) Rate of Benito substituted...

rate(J) = 240 Multiplied!

Using the rate of Juarez we find the time of Juarez:

(240)time(J) = 1440 Substituted...

time(J) = 6 Divided!

And we finally find the time of Benito:

6 = time(B) + 4 Substituted...

time(B) = 2 Subtracted!

So after all those equations and steps, we got the answers, and if we were not of them being correct, all we have to do is check them by substituting them all into the original equation!

Final Answers:

Rate of Benito: 60 Mph

Time of Benito: 2 Hours

Rate of Juarez: 240 Mph

Time of Juarez: 6 Hours

Equations are very important to have, for without them, it is quite impossible to get problems right, for example:

Juarez's speed was 4 times as great as that of Benito. Thus, Juarez could travel 1440 miles in only 4 hours more than it took Benito to travel 120 miles. Find the speed of both and the times of both.

So in this example there are multiple equations to write:

rate(J) * time(J) = 1440 miles Rate * Time = Distance

rate(B) * time(B) = 120 miles Rate * Time = Distance

rate(J) = 4 * rate(B) Rate of Juarez is 4 times the rate of Benito

time(J) = time(B) + 4 Time of Juarez is 4 hours longer than Benito

So by this question we got four equations, and now what we want to do, is to substitute the rate and time of Juarez into the first equation like so:

rate(J) = 4 * rate(B) goes into the rate(J) which was in the first equation so it now is:

4 * rate(B) * time(J) = 1440 Rate of Juarez substituted

And now we substitute the time of Juarez for the time of Benito + 4 :

4rate(B) * [time(B) + 4] = 1440

4rate(B) * time(B) + 16rate(B) = 1440 Multiply...

4(120) + 16rate(B) = 1440 Now substituted with equation 2...

16rate(B) = 1440 - 480 Brought 480 over...

16rate(B) = 960 Subtracted...

rate(B) = 60 Divided!

After finding the rate of Benito we find the rest by using the four equations we got in the beginning:

rate(J) = 4(60) Rate of Benito substituted...

rate(J) = 240 Multiplied!

Using the rate of Juarez we find the time of Juarez:

(240)time(J) = 1440 Substituted...

time(J) = 6 Divided!

And we finally find the time of Benito:

6 = time(B) + 4 Substituted...

time(B) = 2 Subtracted!

So after all those equations and steps, we got the answers, and if we were not of them being correct, all we have to do is check them by substituting them all into the original equation!

Final Answers:

Rate of Benito: 60 Mph

Time of Benito: 2 Hours

Rate of Juarez: 240 Mph

Time of Juarez: 6 Hours