Portion of Swimming Pool Filled in One by Hose = 1/24

1. Your paycheck varies directly as the number of hours you work if your paycheck is $182.60 for 22 hours, find your pay for 10 hours. Your pay is $____

P =kh

182.60 = k*22

P=k*10

182.60/P = 22/10

O, P = 182.60*10/22 = 83

Pay will be $83.
2. One hose can fill a swimming pool in 24 hours. A hose from the neighbor's house can fill the swimming pool in 64 hours. If the two hoses ran at the same time, how long does it take to fill the swimming pool?
It would take ______hours for both hoses running at the same time to fill the swimming pool.
(Simplify your answer. Type an integer, fraction, or mixed number.)

Portion of swimming pool filled in one by hose = 1/24

Portion of swimming pool filled by neighbor’s hose = 1/64

Portion filled by both hoses =

Hence, time taken to fill swimming pool =
3. Jared is training for a cross-country cycling race. He rode 62 miles in 2 hours. After the first 50 miles through the foothills, he increased his speed by 6 mph on flat roads for the last 12 miles. Find Jared's cyclic speed through the foothills.
Jared's cycling speed through the foothills was ______miles per hour. (Simplify your answer.)

62 miles in 2 hours; hence average speed = 62/2 = 31 mph

If speed in 50 miles was v mph, we will have time taken = 50/v

Speed on flat road = v+6; hence, time taken = 12/(v+6).

Total time 2 hrs; hence,

Or, 50v+300+12v= 2v^2+12v

Or, v^2-25v-150=0

Or, v^2-30v+5v-150=0

Or, v(v-30)+5(v-30)=0

Or, (v-30)(v+5) = 0

Or, v =30,-5

Discarding –ve value, we get v = 30mph is the speed through foothill.

4. One hose can fill a swimming pool in 66 hours. A hose from a neighbor's house and build a swimming pool and 77 hours. If the two hoses run at the same time, how long does it take to fill the swimming pool?
(Simplify your answer. Type an integer, fraction, or mixed number.)

Portion of swimming pool filled in one by hose = 1/66

Portion of swimming pool filled by neighbor’s hose = 1/77

Portion filled by both hoses =

Hence, time taken to fill swimming pool =
5. John and Dwight clean an entire building in 2 hours. John can clean the entire building by himself in three fewer hours than Dwight can. How long does it take John to clean the building by himself?
It would take John ______hour(s) to clean the building by himself.
(Simplify your answer.)

Let us assume that John can clean entire building in x hrs.

Hence, building cleaned in 1 hr = 1/x

Time taken by Dwight in cleaning entire building = (x+3)hrs

Hence, building cleaned by Dwight in 1 hr = 1/(x+3)

Hence, building cleaned by both in 1 hr. = 1/x+1/(x+3)

Hence time taken by both to clean entire building =

But both take 2 hrs; hence,

Or, x^2+3x=4x+6

Or, x62-x-6=0

Or, x^2-3x+2x-6=0

Or, (x-3)+2(x-3)=0

Or, (x-3)(x+2)=0

Or, x = 3,-2

Hence, John can clean entire building in 3 hrs. We neglect –ve value.
6. Be some of the reciprocal of a number and 1/7 is 10/21. Find the number. The number is ______.

Let the number = x

Hence,