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Question Number 41912 by pieroo last updated on 15/Aug/18

The estimated time for Abu and Ali to repair a faulty car is six hours. If Abu used 10 hours to repair the car, how many hours will Ali use to repair the car?

$$\mathrm{The}\:\mathrm{estimated}\:\mathrm{time}\:\mathrm{for}\:\mathrm{Abu}\:\mathrm{and}\:\mathrm{Ali}\:\mathrm{to}\:\mathrm{repair}\:\mathrm{a} \\ $$$$\mathrm{faulty}\:\mathrm{car}\:\mathrm{is}\:\mathrm{six}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{Abu}\:\mathrm{used}\:\mathrm{10}\:\mathrm{hours}\:\mathrm{to} \\ $$$$\mathrm{repair}\:\mathrm{the}\:\mathrm{car},\:\mathrm{how}\:\mathrm{many}\:\mathrm{hours}\:\mathrm{will}\:\mathrm{Ali}\:\mathrm{use}\:\mathrm{to}\:\mathrm{repair} \\ $$$$\mathrm{the}\:\mathrm{car}? \\ $$

Answered by MJS last updated on 15/Aug/18

Abu does (1/(10)) car per hour Ali does (1/x) car per hour both do (1/6) car per hour (1/(10))+(1/x)=(1/6) (1/x)=(1/6)−(1/(10))=(1/(15)) x=15 Ali will need 15 hours

$$\mathrm{Abu}\:\mathrm{does}\:\frac{\mathrm{1}}{\mathrm{10}}\:\mathrm{car}\:\mathrm{per}\:\mathrm{hour} \\ $$$$\mathrm{Ali}\:\mathrm{does}\:\frac{\mathrm{1}}{{x}}\:\mathrm{car}\:\mathrm{per}\:\mathrm{hour} \\ $$$$\mathrm{both}\:\mathrm{do}\:\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{car}\:\mathrm{per}\:\mathrm{hour} \\ $$$$\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{{x}}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\frac{\mathrm{1}}{{x}}=\frac{\mathrm{1}}{\mathrm{6}}−\frac{\mathrm{1}}{\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{15}} \\ $$$${x}=\mathrm{15} \\ $$$$\mathrm{Ali}\:\mathrm{will}\:\mathrm{need}\:\mathrm{15}\:\mathrm{hours} \\ $$

Commented by pieroo last updated on 15/Aug/18

thanks a lot sir

$$\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{sir} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 15/Aug/18

Abu repair (1/(10))th portoion of work in 1hour Abu+Ali repair (1/6)th portionlfwork in 1hour so Ali repair((1/6)−(1/(10))) (((5−3)/(30)))=(2/(30))portion of work in1 hour so Ali repair the whole car in ((30)/2)=15 hrs

$${Abu}\:{repair}\:\frac{\mathrm{1}}{\mathrm{10}}{th}\:{portoion}\:{of}\:{work}\:{in}\:\mathrm{1}{hour} \\ $$$${Abu}+{Ali}\:{repair}\:\frac{\mathrm{1}}{\mathrm{6}}{th}\:{portionlfwork}\:{in}\:\mathrm{1}{hour} \\ $$$${so}\:{Ali}\:{repair}\left(\frac{\mathrm{1}}{\mathrm{6}}−\frac{\mathrm{1}}{\mathrm{10}}\right) \\ $$$$\:\:\left(\frac{\mathrm{5}−\mathrm{3}}{\mathrm{30}}\right)=\frac{\mathrm{2}}{\mathrm{30}}{portion}\:{of}\:{work}\:{in}\mathrm{1}\:{hour} \\ $$$${so}\:{Ali}\:{repair}\:{the}\:{whole}\:{car}\:{in}\:\frac{\mathrm{30}}{\mathrm{2}}=\mathrm{15}\:{hrs} \\ $$

Commented by pieroo last updated on 15/Aug/18

thanks sir

$$\mathrm{thanks}\:\mathrm{sir} \\ $$

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