Question

A tank holds 2500 liters of oil. A small pump can add oil at a rate of x liters per minute, and a large pump can add oil at a rate of (x + 20) liters per minute.

(i) Expression for the number of minutes the small pump takes to fill the tank in terms of x.
(ii) Expression for the number of minutes the large pump takes to fill the tank in terms of x.
(iii) An equation relating the time it takes for the small pump and the large pump to fill the tank, showing it simplifies to 3x² + 60x - 10,000 = 0.
(iv) Find the time the large pump takes to fill the tank in minutes and seconds, rounded to the nearest second.

Answer 1

The expression for the number of minutes the small pump takes to fill the tank is t = 2500/x. The expression for the number of minutes the large pump takes to fill the tank is t = 2500/(x+20). The quadratic equation 3x² + 60x - 10000 = 0 relates the time it takes for the small and large pumps to fill the tank.

Step-by-step explanation:

(i) Expression for the number of minutes the small pump takes to fill the tank in terms of x:

The small pump can add oil at a rate of x liters per minute. To fill the tank, you need to divide the tank capacity (2500 liters) by the rate of the small pump. So, the expression would be t = 2500/x.

(ii) Expression for the number of minutes the large pump takes to fill the tank in terms of x:

The large pump can add oil at a rate of (x + 20) liters per minute. To fill the tank, you need to divide the tank capacity (2500 liters) by the rate of the large pump. So, the expression would be t = 2500/(x+20).

(iii) An equation relating the time it takes for the small pump and the large pump to fill the tank:

To find the equation relating the time it takes for the small and large pumps to fill the tank, we can set the expressions from (i) and (ii) equal to each other. So, 2500/x = 2500/(x+20). Simplifying this equation will give you 3x² + 60x - 10000 = 0.

The expression for the number of minutes the small pump takes to fill the tank is t = 2500/x. The expression for the number of minutes the large pump takes to fill the tank is t = 2500/(x+20). The quadratic equation 3x² + 60x - 10000 = 0 relates the time it takes for the small and large pumps to fill the tank.