Question

(Please help my test is timed.) The amount of time, t, Tom needed to mow the grass in his neighborhood is directly proportional to the amount of lawns, I, (all the same size) and inversely as the number of friends, f , who helped Tom. If it takes Tom and one friend 5 hours to mow 10 lawns, how long will it take Tom and 3 friends to mow 24 lawns?

Answer 1

Answer:

Step-by-step explanation:

500 dude

Answer 2

Tom & his 3 friends will take 4 hours to mow 24 lawns.

How to elaborate the problem ?

The amount of time = t

The amount of lawn = l

The amount of time tom needed to mow the grass in his neighborhood is directly proportional to the amount of lawns, i.e. $t\alpha l$

The number of friends = f

The amount of time tom needed to mow the grass in his neighborhood is inversely as the number of friends, i.e. $t\alpha \frac{1}{f}$

∴ $t\alpha \frac{l}{f}$

What is the required time ?

It takes Tom and one friend 5 hours to mow 10 lawns

Let, t = m × $\frac{l}{f}$   , where m is constant of proportional

∴ m = (t × f)/l

⇒ m = (5×1)/10

⇒ m = 5/10

⇒ m = 1/2

Now, Let, Tom and 3 friends to mow 24 lawns in t₁ hours.

∴  t₁ = (m × l)/f

⇒  t₁ = (1/2 × 24)/3

⇒  t₁ = 12/3

⇒  t₁ = 4

So, they will take 4 hours.

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