Question 1185630: I have a word problem here and I having trouble figuring out the let statements and equations to solve the problem. The word problem is:
A boat has two motors, one large and one small. If only the large motor is running. a tank of fuel lasts 2 h. If only the small motor is running, the tank of fuel lasts 4 h.
How long will the fuel last if both motors are running?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! what i get is the following.
rate * time = quantity.
the rate is the rate that the motor empties the tank per hour.
the time is how long it takes to empty the tank.
the large motor empties the tank in 2 hours.
rate * 2 = 1 empty tank.
therefore, it is emptying 1/2 of the tank in one hour.
the small motor empties the tank in 4 hours.
rate * 4 = 1 empty tank.
therefore, it is emptying 1/4 of the tank in one hour.
when they work together, their rates are additive.
you get (1/2 + 1/4) * time = 1 empty tank.
combine fractions to get 3/4 * time = 1 empty tank.
solve for time to get time = 4/3 hours.
you figure it has to be less than 2 hours because the little motor can empty the tank in 2 hours all by itself.
with help from the big tank, the total time has to be less than 2 hours.
in 4/3 hours, the little motor empties 1/4 * 4/3 = 2/6 = 1/3 of the tank.
in the same 4/3 hours, the large motor empties 1/2 * 4/3 = 4/6 = 2/3 of the tank.
their combined work empties 1/3 + 2/3 = 1 = all of the tank in 4/3 hours.
solution makes sense.
i would go with 4/3 hours to empty the tank when both motors are running.
if you let x equal the rate of the large motor and y equal the rate of the small motor, then your equations become:
x * 2 = 1 and y * 4 = 1.
solve for the variables to get:
x = 1/2 and y = 1/4
those are the rates that the large and small motors are emptying the tank.
hen they work together, the formula becomes:
(x + y) * T = 1
since x = 1/2 and y = 1/4, you get:
(1/2 + 1/4) * T = 1
solve for T to get T = 3/4 hours.
let me know if you need more information as to how this was done.
the rates of x and y are how much of the tank has been emptied in one hour.
T is the time it takes to empty the tanks.
Answer by greenestamps(13200)  (Show Source):
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