Roger needs to fill his exmpty fuel carried for an emergency delivery. He has to pumps that can fill the carrier in 2 hours when both used at the same time. Individually, one of the pumps takes 45 mintues less than the other to fill the empty carrier. Suddenly, he realizes that he loaned his faster pump to a friend who is presently out of town. He must rely on the slower pump to do the job. How much time will it take to fill the empty carrier with this slower pump?

Question

Roger needs to fill his exmpty fuel carried for an emergency delivery. He has to pumps that can fill the carrier in 2 hours when both used at the same time. Individually, one of the pumps takes 45 mintues less than the other to fill the empty carrier. Suddenly, he realizes that he loaned his faster pump to a friend who is presently out of town. He must rely on the slower pump to do the job. How much time will it take to fill the empty carrier with this slower pump?

Answer 1

To solve this problem, let's assign variables to the unknown quantities in order to form an equation.

Let's call the time taken by the slower pump alone to fill the empty carrier as "x" hours. Since the slower pump takes 45 minutes more than the faster pump to complete the job, the faster pump would take (x - 45) minutes to fill the carrier on its own.

We know that when both pumps are used together, they can fill the carrier in 2 hours. This means that their combined rate of filling is 1 carrier per 2 hours, or 1/2 carrier per hour.

Now let's set up an equation using the rates of the pumps:
1/x + 1/(x - 45) = 1/2

To solve this equation, we can find a common denominator of (x)(x - 45)(2). Multiplying through by this denominator, we get:
2(x - 45) + 2x = x(x - 45)

Expanding and simplifying the equation yields:
2x - 90 + 2x = x^2 - 45x

Combining like terms and bringing all terms to one side, we have a quadratic equation:
x^2 - 49x + 90 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Factoring is not straightforward here, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

For our quadratic equation, the coefficients are:
a = 1, b = -49, c = 90

Substituting these values into the quadratic formula, we get:
x = (-(-49) ± √((-49)^2 - 4(1)(90))) / (2(1))

Simplifying further:
x = (49 ± √(2401 - 360)) / 2
x = (49 ± √2041) / 2

Since we are interested in the positive value of x, we can disregard the negative solution:
x = (49 + √2041) / 2

Calculating this value, we find that x is approximately 49.08.

Therefore, it will take approximately 49.08 hours to fill the empty carrier using the slower pump alone.

Answer 2

Hunter Cox / Jackson Welch / Kristie Dexter / Maddi Donald --

All posting from the same computer ... all not following directions on the Post a New Question page ... and all not getting help because of these things.

Hmmm.