FCTC FCTC Test Firefighter Mathematical Problems Questions and Answers 3

Question 1

Water pressure in a hose is 80 psi at street level. For every 10 feet of elevation gained, pressure drops 4.34 psi. What is the pressure at a nozzle 50 feet above street level?

Accepted Answer

58.3 psi

Answer

Pressure loss = (50/10) × 4.34 = 21.7 psi; 80 − 21.7 = 58.3 psi.

Question 2

A fire department responds to 1,248 calls in a year. If 37.5% are false alarms, how many calls are actual emergencies?

Accepted Answer

780 calls

Answer

1,248 × (1 − 0.375) = 1,248 × 0.625 = 780 actual emergency calls.

Question 3

A cylindrical water tank has a radius of 5 feet and a height of 12 feet. Using π ≈ 3.14, what is the volume of the tank in cubic feet?

Accepted Answer

942 cubic feet

Answer

Volume = π × r² × h = 3.14 × 25 × 12 = 942 cubic feet.

Question 4

A firefighter uses an air cylinder that lasts 30 minutes at a normal work rate. If the firefighter is working at high exertion and the cylinder lasts only 65% as long, how many minutes will it last?

Accepted Answer

19.5 minutes

Answer

30 × 0.65 = 19.5 minutes at high exertion.

Question 5

A fire hose 200 feet long loses 5 psi of friction per 50 feet of hose. If the pump supplies 120 psi, what is the nozzle pressure?

Accepted Answer

100 psi

Answer

Friction loss = (200/50) × 5 = 20 psi; nozzle pressure = 120 − 20 = 100 psi.

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FCTC FCTC Test Firefighter Mathematical Problems Questions and Answers 3