SOLUTION: Sorry there is no ISBN of this textook. "Will you solve this Word problem please" 1. A, B, and C can finish a job in 6 days. If B & C work together, the job will take 9 days

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Sorry there is no ISBN of this textook. "Will you solve this Word problem please" 1. A, B, and C can finish a job in 6 days. If B & C work together, the job will take 9 days      Log On

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Question 85255: Sorry there is no ISBN of this textook.
"Will you solve this Word problem please"
1. A, B, and C can finish a job in 6 days. If B & C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?

2. A bicyclist and a hiker leave at the same place at the same time and travel in the same direction. The bicyclist travel three times as fast as the hiker. at the end of 3 hr they are 24 miles apart. how fast does the hiker travel.

3. A person travelling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have travelled only 1315
miles in the same length of time. Find the speed of the plane and the ship.

Thank you so much.

Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
1. Create a system of equations based on what portion of the job each group can do in 1 day:
A + B + C = 1%2F6 [together, they can do 1%2F6 of the job per day]
B + C = 1%2F9 [together, B and C can do 1%2F9 of the job per day]
A + C = 1%2F8 [together, A and C can do 1%2F8 of the job per day]
Combine the first two equations to eliminate B and C and solve for A:
A + B + C = 1%2F6
-B - C = -1%2F9
________________________
A = 3%2F54
A alone can do 3%2F54 of the job per day so it'll take A 54%2F3 = 18 days to do the job alone
Now, plug 3%2F54 or 1%2F18 into the third equation for A and solve for C:
1%2F18 + C = 1%2F8
C = 1%2F8 - 1%2F18 = 5%2F72
C alone can do 5%2F72 of the job per day so it'll take C 72%2F5 = 142%2F5 days to do the job alone
Now, plug 5/72 into the second equation for C and solve for B:
B + 5%2F72 = 1%2F9
B = 1%2F9 - 5%2F72 = 3%2F72
B alone can do 3%2F72 of the job per day so it'll take B 72%2F3 = 24 days to do the job alone