SOLUTION: Tom is twice as productive as Bill and half as productive as Ted. If Bill produces 18 units, how many units will Ted produce?

Question 1027130: Tom is twice as productive as Bill and half as productive as Ted. If Bill produces 18 units, how many units will Ted produce?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = quantity.

for bill, we let r = his rate and t = his time and 18 = his quantity to get:

r * t = 18.

we can solve for time he takes to get t = 18/r.

tom works twice as fast as bill.

his rate is equal to 2r.

since the time he takes is the same as the time bill takes, his time is equal to 18/r.

the rate * time = quantity formula for tom becomes:

2r * 18/r = q, where q is equal to the quantity that tom produces.

simplify this formula to get 36r/r = q which results in q = 36.

in the same time, tom is twice as productive so his rate is equal to twice as many units in the same time and he can therefore produce 36 units in the same time that bill produces 18 units.

since tom is half as productive as ted, then, by using the same logic, ted must have produced 72 units in the same time that tom produced 36.

the rate * time formula is used again.

the time is the same as bill's which was 18/r (it's the same for everybody).

the rate for tom is half the rate of ted's.

since the rate for tom is equal to 2r, then the rate for ted must be equal to 4r.

the rate * time formula for ted becomes:

4r * 18/r = q

this becomes 72r/r = q which simplifies to 72 = q.

the solution is:

tom produces 36 units in the same time that bill produces 18.
ted produces 72 units in the same time that bill produces 18.

tom produces twice as many units as bill and half as many units as ted.

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