who says you can't do rocket science?

Question

in this class activity, use Polya's problem-solving steps to make progress on solving the next problem. Then explain why the conclusions you have reached are true, whether or not your conclusions fully solve the problem. Problem: A rocket can use two different types of fuel. Rocket scientists know that it takes 30 minutes to fill the fuel tank with type A fuel from a type A hose, whereas it takes 45 minutes to fill the same fuel tank with type B fuel from a type B hose. The type B hose is smaller than the type A hose. The rocket's fuel tank will now be filled simultaneously with type A and type B fuels, each flowing out of their own hoses at a constant rate. How long will it take to fill the fuel tank? Before you attempt to find an exact answer, determine approximately how long it should take for the fuel tank to fill. Answer this either with a specific number of minutes, or by saying, "It will take less than... minutes, but more than... minutes, to fill the tank." In either case, explain your reasoning. 

Answer 1

GIVEN:

It takes 30 minutes to fill the tank with Fuel A using Hose A.

It takes 45 minutes to fill the tank with Fuel B using Hose B.

 

FIND:
Amount of time it will take to fill the tank with A and B simultaneously.

 

METHOD AND REASONING:

If takes 30 min for A to fill the tank, then it can fill 1/30th of a tank in 1 minute.

A = 1/30

 

If takes 45 min for A to fill the tank, then it can fill 1/45th of a tank in 1 minute.

B = 1/45

 

If we fill the tank with A and B simultaneously, then in one minute:

A + B

= 1/30 + 1/45

= 1/30 * (3/3) + 1/45 * (2/2)

= 3/90 + 2/90

= 5/90

= 1/18

 

So if we fill up the tank and both hoses, 1/18th of a tank will be filled in one minute.

 

If 1/18th of a tank will be filled in one minute, then it will take 18 minutes to fill the tank.

 

ANSWER:

18 minutes