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It-takes-Musa-3-days-to-buid-a-room-while-it-takes-John-4-days-How-many-days-will-it-takes-both-of-them-




Question Number 120502 by Engr_Jidda last updated on 31/Oct/20
It takes Musa 3 days to buid a room  while it takes John 4 days.  How many days will it takes both of them?
$$\mathrm{It}\:\mathrm{takes}\:\mathrm{Musa}\:\mathrm{3}\:\mathrm{days}\:\mathrm{to}\:\mathrm{buid}\:\mathrm{a}\:\mathrm{room} \\ $$$$\mathrm{while}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{John}\:\mathrm{4}\:\mathrm{days}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}? \\ $$
Answered by Olaf last updated on 31/Oct/20
3×4 = 12.  It takes Musa 12 days to build 4 rooms.  It takes John 12 days to build 3 rooms.  ⇒ It takes Musa & John 12 days to  build 7 rooms.  ⇒ It takes Musa & John ((12)/7) days to  build 1 room.
$$\mathrm{3}×\mathrm{4}\:=\:\mathrm{12}. \\ $$$$\mathrm{It}\:\mathrm{takes}\:\mathrm{Musa}\:\mathrm{12}\:\mathrm{days}\:\mathrm{to}\:\mathrm{build}\:\mathrm{4}\:\mathrm{rooms}. \\ $$$$\mathrm{It}\:\mathrm{takes}\:\mathrm{John}\:\mathrm{12}\:\mathrm{days}\:\mathrm{to}\:\mathrm{build}\:\mathrm{3}\:\mathrm{rooms}. \\ $$$$\Rightarrow\:\mathrm{It}\:\mathrm{takes}\:\mathrm{Musa}\:\&\:\mathrm{John}\:\mathrm{12}\:\mathrm{days}\:\mathrm{to} \\ $$$$\mathrm{build}\:\mathrm{7}\:\mathrm{rooms}. \\ $$$$\Rightarrow\:\mathrm{It}\:\mathrm{takes}\:\mathrm{Musa}\:\&\:\mathrm{John}\:\frac{\mathrm{12}}{\mathrm{7}}\:\mathrm{days}\:\mathrm{to} \\ $$$$\mathrm{build}\:\mathrm{1}\:\mathrm{room}. \\ $$
Answered by bemath last updated on 01/Nov/20
let x is day it takes both of them   we get (1/x) = (1/4)+(1/3)=(7/(12))  so x = ((12)/7) day
$$\mathrm{let}\:\mathrm{x}\:\mathrm{is}\:\mathrm{day}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}\: \\ $$$$\mathrm{we}\:\mathrm{get}\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{7}}{\mathrm{12}} \\ $$$$\mathrm{so}\:\mathrm{x}\:=\:\frac{\mathrm{12}}{\mathrm{7}}\:\mathrm{day} \\ $$

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