Pre-Calc Word Problem Help
I need help on word problems in my math book, I still have problems understanding how to do "mixture problems and sharing job problems." Please offer any tips possible in getting better at solving them.
55. The radiator in a car is filled with 60% antifreeze and 40% water, it is recommended to have the concentration of antifreeze in the summer at 50%. If the capacity of the radiator is 3.6 liters, how much antifreeze needs to be drained and replaced with water to reduce the antifreeze concentration?
*for this I drew a diagram, and thought it was a simple, remove the 10% of anti and put in 10% of water which is 0.36L of each, so I thought the answer was 0.36 had to be removed and 0.36 put in. But the answer was 0.6L, that I don't understand.
59. Candy and Tim share a paper route, it takes Candy 70 minutes to finish the route and 80 minutes for Tim to finish. How long will it take if they both work together?
Uhm, I knew if they both worked together then, Candy can finish half the route in 35 min and Tim in 40 min, and the mid-point of those times is 37.5 min, but the answer was 37 min and 20 seconds. 20 seconds/60seconds = 1/3 not 1/2... Im confused.
61. Betty and Karen are painting a house. Working together they can finish painting 2/3 of the time it takes Karen ALONE. Betty takes 6 hours working ALONE. How long does it take Karen to finish painting a house ALONE?
Okay so I gave a variable to both, B and K > B + K = 2/3K ? and B = 6 > so 6 + K = 2/3K > *3 > 18 + 3K = 2K > and -18 = K?
This I didn't understand.
62. Bob and Jim use hoses to fill up Bob's swimming pool. Both hoses take 18 hours to fill the pool. Bob's hose, used ALONE, takes 20% less of the time than Jim's hose ALONE. How much time is required to fill the pool by each hose alone?
Okay so I did this: B + J = 18 and B = 0.2(J) ? > So I substituted the B in the first equation > 0.2(J) + J = 18 > J = 15?
And that doesnt make sense...
Thanks in advance, please show how you did the problems.