Not enough information?

[Motherof8]

A can complete a piece of work in 21 hours. With the help of A, B can do it in 6 1/4 hrs. less time than he could do it alone. How many hrs. does B need to do it alone? What kind of equation do you need to solve this problem?

[stapel_eliz]

A can complete a piece of work in 21 hours. With the help of A, B can do it in 6 1/4 hrs. less time than he could do it alone. How many hrs. does B need to do it alone? What kind of equation do you need to solve this problem?

To learn how to set up and solve this sort of exercise, please try this lesson.

Then use the set-up explained and demonstrated in the lesson:

. .. .time to complete task (hours):
. . . . .A: 21
. . . . .B: b
. . . . .together: b - 6.25

. . .completed per time unit (hours):
. . . . .A: 1/21
. . . . .B: 1/b
. . . . .together: ...

...and so forth.

[Motherof8]

I used this equation: 1/21 +1/b = 1/b-6.25, tried to have it worked out on Mathway and was told it had no solution.

[stapel_eliz]

I used this equation: 1/21 +1/b = 1/b-6.25, tried to have it worked out on Mathway and was told it had no solution.

If you entered the equation as you've posted above (that is, without grouping symbols for the denominator on the right-hand side), then there clearly is no solution.

However, if you multiply through to clear the denominators, you will find that you get a quadratic equation that is quite solveable.