word problems

Question

Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 5 more days than the other?

Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 5 more days than the other?

Answer 1

Time taken by 2 constructor  to finish the work =6 days

time taken by first constructor = x days

time taken by second constructor = x+5 days

 

2 constructor 1 day work = 1/6

 

first constructor 1 day work = 1/x

second constructor 1 day work = 1/(x+5)

 

so first constructo 1 day work + second constructor 1 day work = 2 constructor 1 day work

 

                                 1/x   + 1/(x+5)  = 1/6

 

              

                                  6(x+5) + 6x = x(x+5)

                            

                                   6x+30 +6x =x² + 5x

 

 

                                    12x +30 =x² +5x

 

                                   x² -7x -30 = 0

 

                                 (x-10)(x+3)=0

 

                                 x=10 or x=-3

 

time taken by first constructor = x days = 10 days
time taken by second constructor = x+5 days =10+5=15 days