Question 66756: 36.Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith's. How fast was each one traveling?
62. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
The answer is 90 minutes can you help to setup and solve this expression?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! 36.Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith's. How fast was each one traveling?
Let r=Smith's speed
and t=Smiths time (hrs)
Then r+5=Jones speed
and t+.5=Jones time (hr)
Distance (d)=rate(or speed) (r)*time (t)or d=rt
Smith's distance: 45=rt
Jones' distance: 70=(r+5)(t+.5)
So our two equations to solve are:
(1) 45=rt
(2) 70=(r+5)(t+.5)
expand (2)
(2) 70=rt+5t+.5r+2.5
Divide both sides of (1) by r and we get:
t=45/r; substitute in (2)
70=(45/r)(r)+5(45/r)+.5r+2.5 simplifying, we get:
70=45+225/r+.5r+2.5 and this equals:
70=47.5+225/r+.5r subtract 47.5 from both sides
22.5=225/r+.5r multiply every term by r
22.5r=225+.5(r^2) divide each term by .5
45r=450+r^2 subtract 45r from both sides
r^2-45r+450=0
Use quadratic formula:
r=(45+or-sqrt(2025-1800))/2;
r=(45+or-sqrt(225))/2;
r=(45+or-15)/2
r=(45+15)/2 =60/2;
r=30 mph-------------Smith's speed
r+5=35 mph-----------Jones' speed
and
r=(45-15)/2=30/2;
r=15 mph-------------Smith's speed
r+5=20 mph------------Jones' speed
CK
The rate condition is satisfied by both solutions.
We now need to check to see if the time condition is also satisfied.
r=30 mph-------------Smith's speed
r+5=35 mph-----------Jones' speed
Smith's time=45/30=1.5 hours
Jones' time=70/35=2 hours
The time condition is met.
r=15 mph-------------Smith's speed
r+5=20 mph------------Jones' speed
Smith's time=45/15=3 hours
Jones time=70/20=3.5 hrs
The time condition is also met.
Both solutions are valid.
62. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
The answer is 90 minutes can you help to setup and solve this expression?
Here, we are given all the information we need to solve the problem----There's not really anything to set up
rate at which the tank fills =1/45 cu units per min
rate at which the tank empties=1/30 cu units per min
If both pipes are open, the rate at which the tank empties is the difference between the rate at which it fills and the rate at which it empties, or:
1/30-1/45 the LCM is 90 so we have
(3-2)/90=1/90
If both pipes are open, the rate at which the tank empties =1/90 cu units/min
Therefore, It completely empty in 90 min
Hope this helps---ptaylor
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