Question 1023795
1. One inlet pipe can fill an empty pool in 6 hours, and a 
drain can empty the pool in 8 hours. How long will it take 
the pipe to fill the pool if the drain is left open? 
<pre>
               Part of pool   =   Rate in   times  Time in
                filled            pool/hr           hours   
Inlet pipe         1                1/6               6
Outlet pipe       -1               -1/8               8
Both open          1                1/T               T

Rate of Inlet + Rate of outlet = Together rate
       1/6    +   (-1/8)       =  1/T

Multiply by 24T
   
       4T    -       3T        =  24
                      T        =  24

It'll take 24 hours. 
</pre>                       
2. Hannah can paint a room in 8 hours. Destiny can paint 
the same room in 6 hours. How long does it take for both 
Hannah and Destiny to paint the room it they are working 
together? 
<pre>
               Part of room       Rate in         Time in
                 painted          room/hr           hours   
Hannah             1                1/6               6
Destiny            1                1/8               8
Both painting      1                1/T               T

Rate of Hannah + Rate of Destiny = Together rate
       1/6    +        1/8       =  1/T

Multiply by 24T
   
       4T    +       3T        =  24
                     7T        =  24
                      T        =  24/7 or 3 3/7 hours.  
It'll take 3 3/7 hours. 
</pre>
3.A plane can fly 360 miles in the same time as it 
takes a car to go 90 miles. If the car travels 
90 mph slower than the plane, find the speed of 
the plane. 
<pre>
          Distance   =    Rate in       Time in
          traveled       miles/hour     hours = dist./rate   
Plane        360              x           360/x
Car           90             x-90        90/(x-90)


          Plane's time = Car's time.

                 360/x = 90/(x-90)

Cross multiply

             360(x-90) = 90x
            360x-32400 = 90x
                  270x = 32400
                     x = 32400/270
                     x = 120 miles/hour

Edwin</pre>