ACT Math Practice Question – Rates

Published on Saturday, July 6th, 2013 by

A sink hole with a depth of 450 cm is being filled in at a rate of 2 cm per week. The depth of another nearby sinkhole is 500 cm, and it is being filled at a rate of 4 cm per week. Assuming the sinkholes continue to be filled at these constant rates, in about how many weeks will the two sinkholes have the same depth?

A. -25
B. 20
C. 25
D. 30
E. 40

Scroll down for the problem with solution.

A sink hole with a depth of 450 cm is being filled in at a rate of 2 cm per week. The depth of another nearby sinkhole is 500 cm, and it is being filled at a rate of 4 cm per week. Assuming the sinkholes continue to be filled at these constant rates, in about how many weeks will the two sinkholes have the same depth?

A. -25

B. 20

C. 25

D. 30

E. 40

The correct answer is C. Express this word problem as an equation:

450 – 2x = 500 – 4x

Add 4x to both sides.

450 + 2x = 500

Subtract 450 from both sides.

2x = 50

x = 25


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