How long would it take Bobby

Question

Twin brother billy and bob can mow their grandparents lawn together for 83 minutes billy could mow the lawn for 10 minutes less time that it would take Bobby how long would it take Bobby to mow the lawn himself

Answer 1

Hello!

Since both Billy and Bobby start with the letter B, let's use other variables to represent them.

x = Billy - aka - how many minutes it takes Billy to mow the lawn alone

y = Bobby - aka - how many minutes it takes Bobby to mow the lawn alone

Together they mow the lawn in 83 minutes, so putting that in "math" language, we have:

x + y = 83

We also know that Billy mows faster. (Billy can mow it in 10 minutes less time than Bobby.)

So who takes longer to mow? That's right, Bobby!

So Bobby's time plus 10 minutes = Billy's time. Put that into "math". Remember our variables from the top.

y + 10 = x

Now we have two equations with two variables in each one. What is this called? A system!

Let's use substitution to solve the system.

x + y = 83

y + 10 = x

Instead of saying "x" in the first equation I'm going to say "y +10" because they are equal (same thing).

(y + 10) + y = 83 Combine Like Terms

2y + 10 = 83 Subtract 10 over to the other side

2y = 73 Finally, divide by 2 to get y by itself

y = 36.5 minutes

What does this mean? Let's put it back in terms of the problem. Bobby (y) can mow the lawn by himself in 36.5 minutes! Great job.

Check It!!!!!

Bobby and Billys time together must be 83, so if Bobby's time is 36.5, what is Billy's time?

That's right, subtract. 83 - 36.5 = 46.5.

Bobby's time plus Billy's time equals 83 (36.5 +46.5 = 83).

Bobby must also be 10 minutes slower than Billy. Is he? Great job!

I hope that helps! Let me know if you have any questions.

-Margaret