Question

Three commercials are played in a row between songs on the radio. The three commercials fill exactly 3 minutes of time. if the commercial uses 1 and 1/6, minutes and the second uses 3/5 minute, how long is the third commercial?

Answer 1

2/9 is the answer
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Answer 2

`Third\ commerical\ takes\ 1 (7)/(30)\ minute.`

Explanation:

Let us assume that the third commerical played time be x .

As given

Three commercials are played in a row between songs on the radio.

The three commercials fill exactly 3 minutes of time.

`if\ the\ commercial\ uses\ 1 (1)/(6)\ minutes\ and\ the\ second\ uses\ (3)/(5)\ minute.`

i.e

`if\ the\ commercial\ uses\ (7)/(6)\ minutes\ and\ the\ second\ uses\ (3)/(5)\ minute.`

Thus equation becomes

`(7)/(6) + (3)/(5) + x = 3`

L.C.M of (6,5) = 30

`(7* 5+ 3* 6+30x)/(30) = 3`

`(35+18+30x)/(30) = 3`

35 + 18 + 30x = 3 × 30

35 + 18 + 30x = 90

30x= 90 -53

30x = 37

`x = (37)/(30)\ minute`

Or

`x =1 (7)/(30)`

`Therefore\ third\ commerical\ takes\ 1 (7)/(30)\ minute.`