# pump in plant Q1

#### jwednesday

##### New member
Algebraic word question - a power plant has been operating continuously for 72 hours. A particular pump in the plant has been operating for only 19 hours. How much longer will both the plant and pump have to operate, until the pump will have operated half as long as the plant?

I know the answer but not sure how to set up the question. I think X would be the Plant and the Pump X + 17?

#### Subhotosh Khan

##### Super Moderator
Staff member
jwednesday said:
Algebraic word question - a power plant has been operating continuously for 72 hours. A particular pump in the plant has been operating for only 19 hours. How much longer will both the plant and pump have to operate, until the pump will have operated half as long as the plant?

I know the answer but not sure how to set up the question. I think X would be the Plant and the Pump X + 17?
X would be amount of TIME the Plant has been operating

(X - 72 + 19) would be amount of TIME the pump has been operating [edited]

the pump will have operated half as long as the plant

Please share with us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

#### jwednesday

##### New member
Thank you for your help. I know the answer is 34 but would it be

(72 - 19 + x) + x = 34
---
2

where by x / 2 is the amount of time the pump would be working? not sure how to make both sides represent the correct time.

#### Subhotosh Khan

##### Super Moderator
Staff member
Subhotosh Khan said:
jwednesday said:
Algebraic word question - a power plant has been operating continuously for 72 hours. A particular pump in the plant has been operating for only 19 hours. How much longer will both the plant and pump have to operate, until the pump will have operated half as long as the plant?

I know the answer but not sure how to set up the question. I think X would be the Plant and the Pump X + 17?
X would be amount of TIME the Plant has been operating

( X + 19 - 72) would be amount of TIME the Pump has been operating

the pump will have operated half as long as the plant

Then

X = 2 * (X - 53)

X = 2X - 106

X = 106

Then additional time for pump and plant to operate = 106 - 72 = 34 hours[/spoiler:33qyydcq]

Check

After 34 additional hours - the plant has operated for (72 + 34 =) 106 hours

After 34 additional hours - the pump has operated for (19 + 34 =) 53 hours

2 * 53 = 106............. Checks