Question

Brad can make 4 key chains in an hour. Velma can make only 3 key chains in an hour, but she already has 6 completed key chains. Explain to Brad how he can use a system of equations to determine when he will have the same number of key chains as Velma. Use complete sentences.

Answer 1

Brad makes 4 per hour, and he has none now.
The number he will have in H hours from now will be B = 4H .

Vera makes 3 per hour, and she has 6 now.
The number she will have in H hours from now will be V = 3H + 6 .

In how many hours from now will Brad and Vera have the same number ?
That means: What will H be when B=V ?

Starting now, 4H = 3H + 6

Subtract 3H from each side: H = 6 hours.

Well that didn't take much work !

In 6 hours from now:

Brad will have B = 4H = 4(6) = 24
Vera will have V = 3H + 6 = 3(6) + 6 = 24

That moment of equality, when Brad catches up to Vera,
will arrive in exactly 6 hours from now. After that, Brad will
pass Vera, and be ahead of her. So, before that happens,
I think they should both take a break, go have ice cream
together, and maybe take the rest of the day off.