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?
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.
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?
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.
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.
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