Question

It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own.

Answer 1

1) Let x the time needed by John to complete the job, so
the time needed by Brian to complete the job will be x+15

2) The rate per hour for John to complete the job is 1/x
The rate per hour for Brian to complete the job is 1/(x+15)

3) But the rate per hour to complete the job is 1/4

Hence we have the following equation:

1/x + 1/(x+15) = 1/4 . Reduce to the same denominator and you will get:
4(x+15) + 4x = x(x+15). Solve for x:

x²+7x - 60 = 0 . Quadratic equation. Use the formula to find the roots:

x' = [-b+√(b²-4.a.c)]/2a and x' = [-b-√(b²-4.a.c)]/2a

x' = 5 and x" = -12 (extraneous)

Then John alone he will complete the job in 5 hours
an Brian alone he will complete the job in 20 hours

Both will complete the job in 4 hours

Proof:

1/5 + 1/20 = 5/20 = 1/4