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Question

Soloving a word problem using a system of linear equations.

Two rainstorms occurred in one week in a certain area. In the first rainstorm 20 ml of rain fell per hour, and in the second rainstorm 25 ml of rain fell per hour. Rain fell that week for a total of 50 hours for a total rainfall of 1175 ml. How long was each of the two rainstorms?

Answer 1

OK, call the amounts of rain R1 and R2, and the lengths of time for which it rained T1 and T2. We're told that R1 = 20T1, R2 = 25T2, R1 + R2 = 1175, and T1 + T2 = 50.

Start by rearranging the last equation and then plugging it into the first one. T1 = 50 - T2; R1 = 20(50 - T2) = 1000-20T2. Now plug that and the second equation into the third one: 1000 - 20T2 + 25T2 = 1175. So 1000 + 5T2 = 1175. Subtract 1000 from each side: 5T2 = 175. Divide by 5: T2 = 35.

Now plug that back into the fourth equation: T1 = 50 - T2 = 50 - 35 = 15.

Finally, check your work. In the first storm it rained 20 mL/hour for 15 hours, producing 300 mL. In the second storm it rained 25 mL/hour for 35 hours, producing 875 mL. The total rainfall was 875 + 300 = 1175, which is what we expected.

The first storm lasted 15 hours; the second, 35.

Answer 2

20 x +25 y =1175

x duration of rain fall of 20 ml/h
y duration of rain fall of 25 ml/h

and x+y =50 sum of duration or x=50-y

20 (50-y) +25 y =1175

1000 -20y +25y =1175

5y = 175

y =35

x= 50-35 =15

Answer 3

h1 = hours of first rainstorm
h2 = hours of second rainstorm

given:
1: (20 * h1) + (25 * h2) = 1175

given:
2: h1 + h2 = 50
then,
3: h2 = 50 - h1

substitute 3: into 1:
4: (20 * h1) + (25 * (50 - h1)) = 1175
then,
5: 20h1 + 1250 - 25h1 = 1175
solving for h1:
6: -5h1 = 1175 - 1250
7: h1 = 75/5
8: h1 = 15 hours **answer**
solving for h2 using equation 2:
9: 15 + h2 = 50
and
10: h2 = 35 hours **answer**

Hope this helps!