Question

Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger's work in 10 days is equal to the first digger's work in 14 days. How many metres does the first digger dig per shift?

Answer 1

Answer:

15

Step-by-step explanation:

Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than  the second as the second digs more than the first. The third digger's work in 10 days is equal to the first digger's work in 14 days. How many metres does the first digger dig per shift?

Let a,b,c be the diggers. Let x be the difference. Given 3 rd digger digs as many metres more than second digs more than the first.

So 324 / 6 = 54 and 54 / 3 = 18

Then x = c – b = b – a.      

Now the first digger digs will be a = b – x = 18 m – x

Third digger digs will be c = b + x = 18 m + x.

Now we know that 10 c = 14 a or 7a = 5c we get

                  5c = 7a

            5(18 m + x) = 7(18 m – x)

          90 m + 5x = 126 m – 7x

        12 x = 36 m

           Or x = 3 m

Now we get a = 18 m – 3m = 15 m