SOLUTION: A construction firm has two tractors T one , and T two. both tractors working together can complete a piece of work in 6 days, while T one alone can complete the work in 15 days.

Question 1149972: A construction firm has two tractors T one , and T two. both tractors working together can complete a piece of work in 6 days, while T one alone can complete the work in 15 days. after the two tractors had worked together for 4 days, tractor T one broke down. find the time taken by tractor T two to complete the remaining work
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A construction firm has two tractors T one , and T two. both tractors working together can complete a piece of work in 6 days, while T one alone can complete the work in 15 days.
after the two tractors had worked together for 4 days, tractor T one broke down. find the time taken by tractor T two to complete the remaining work
:
let x = time required by T2 working alone to do the job
let the completed job = 1
:
each will do a fraction of the job, the two fractions add up to 1
:
Find how long for T2 to the do job alone
+ = 1
multiply by 15x, cancel the denominators
6x + 15(6) = 15x
90 = 15x - 6x
90 = 9x
x = 90/9
x = 10 days T2 working alone
:
let y = time required for T2 to complete the job after 4 hrs
+ = 1
multiply by 30, cancel the denominators
2(4) + 3(y+4) = 30
8 + 3y + 12 = 30
3y = 30 - 20
3y = 10
y = 10/3
y = 3 days for T2 to complete the job

Check in the equation using a calc:
+ =
+ =
.267 + .733 = 1
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
RATES OF WORK
T_one,
T_two,
T_combined,

x, unknown time for T_one to finish

Use the rates to solve for w.
Substitute in the "to finish" equation and simplify and solve for x.
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