Question

Two rainstorms occurred in one week. First storm 15 mL of rain fell per hour. Second storm 30 mL of rain fell per hour. The rain lasted for a total of 70 hours with a total of 1500 mL. What was the duration of each storm?

Answer 1

The first rainstorm lasted for 40 hours and the second rainstorm lasted for 30 hours. A system of equations method was used to find the duration of each storm.

Step-by-step explanation:

Calculating Duration of Rainstorms

Let's denote the duration of the first storm as x hours and the second storm as y hours. The total amount of rain for the first storm would then be 15 mL/hour × x hours and for the second storm 30 mL/hour × y hours. Given that the total duration of the rain is 70 hours, we can set up the following equation: x + y = 70. Additionally, since the total volume of rain is 1500 mL, we have 15x + 30y = 1500.

We can solve this system of equations by multiplying the first equation by 15 to eliminate variable y: 15x + 15y = 1050 and then subtracting this from the second equation: (15x + 30y) - (15x + 15y) = 1500 - 1050, which simplifies to 15y = 450. Thus, y = 30 hours. Finally, we substitute y into x + y = 70 to find x: x = 70 - 30, so x = 40 hours.

Hence, the first storm lasted for 40 hours and the second storm lasted for 30 hours.

Answer 2

The answer to your question is the first rain lasted 40 hours and the second rain lasted 30 hours.

Step-by-step explanation:

Data

1st 15 ml/h = x

2nd 30 ml/h = y

Total time = 70 h and 1500 ml

1.- Write 2 equations

First rain + second rain = 70 h

x + y = 70 (I)

15x + 30 y = 1500 (II)

2.- Solve equations by elimination

Multiply first equation by -15

-15x - 15y = - 1050

15x + 30y = 1500

0x + 15y = 450

y = 450 / 15

y = 30 h

x + 30 = 70

x = 70 - 30

x = 40 h

3.- Conclude

The first rain lasted 40 h and the second rain lasted 30 h.