Question-13756

Question Number 13756 by Tinkutara last updated on 23/May/17

Commented by ajfour last updated on 23/May/17

Commented by ajfour last updated on 23/May/17

15t_1 =5t_1 +5t_2 ⇒ t_2 =2t_1 ......(i) 5t_2 +5t_3 =15t_3 ⇒ 2t_3 =t_2 ....(ii) (i) and (ii) ⇒ t_3 =t_1 let T=t_1 +t_2 +t_3 =t_1 +2t_1 +t_1 =4t_1 15t_1 +15t_3 =40 .....(iii) ⇒30t_1 =40 t_1 =(4/3)h =1h 20min bicycle unused for time = t_2 =2t_1 =2h 40min average speed of tourists for the journey = ((40km)/(4t_1 )) =((40km)/((16/3)h)) =7.5 km/h .

$$\mathrm{15}{t}_{\mathrm{1}} =\mathrm{5}{t}_{\mathrm{1}} +\mathrm{5}{t}_{\mathrm{2}} \\ $$$$\Rightarrow\:{t}_{\mathrm{2}} =\mathrm{2}{t}_{\mathrm{1}} \:\:\:\:\:\:……\left({i}\right) \\ $$$$\mathrm{5}{t}_{\mathrm{2}} +\mathrm{5}{t}_{\mathrm{3}} =\mathrm{15}{t}_{\mathrm{3}} \\ $$$$\Rightarrow\:\:\mathrm{2}{t}_{\mathrm{3}} ={t}_{\mathrm{2}} \:\:\:\:….\left({ii}\right)\: \\ $$$$\left({i}\right)\:{and}\:\left({ii}\right)\:\Rightarrow\:\:{t}_{\mathrm{3}} ={t}_{\mathrm{1}} \\ $$$${let}\:{T}={t}_{\mathrm{1}} +{t}_{\mathrm{2}} +{t}_{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:={t}_{\mathrm{1}} +\mathrm{2}{t}_{\mathrm{1}} +{t}_{\mathrm{1}} =\mathrm{4}{t}_{\mathrm{1}} \\ $$$$\mathrm{15}{t}_{\mathrm{1}} +\mathrm{15}{t}_{\mathrm{3}} =\mathrm{40}\:\:\:…..\left({iii}\right) \\ $$$$\Rightarrow\mathrm{30}{t}_{\mathrm{1}} =\mathrm{40} \\ $$$${t}_{\mathrm{1}} =\frac{\mathrm{4}}{\mathrm{3}}{h}\:=\mathrm{1}{h}\:\mathrm{20}{min} \\ $$$${bicycle}\:{unused}\:{for} \\ $$$$\:\:{time}\:=\:{t}_{\mathrm{2}} =\mathrm{2}{t}_{\mathrm{1}} =\mathrm{2}{h}\:\mathrm{40}{min} \\ $$$${average}\:{speed}\:{of}\:{tourists} \\ $$$$\:{for}\:{the}\:{journey}\:=\:\frac{\mathrm{40}{km}}{\mathrm{4}{t}_{\mathrm{1}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{40}{km}}{\left(\mathrm{16}/\mathrm{3}\right){h}}\:=\mathrm{7}.\mathrm{5}\:{km}/{h}\:. \\ $$

Commented by Tinkutara last updated on 23/May/17

$$\mathrm{Thanks}! \\ $$

Commented by ajfour last updated on 23/May/17

$${could}\:{you}\:{follow}\:{my}\:{solution}\:? \\ $$

Commented by Tinkutara last updated on 23/May/17

$$\mathrm{Yes}\:\mathrm{I}\:\mathrm{completely}\:\mathrm{understood}.\:\mathrm{Thanks}. \\ $$

Answered by ajfour last updated on 23/May/17

$$\left.{Q}.\mathrm{12}\right)\:\:\left(\mathrm{4}\right)\:\mathrm{7}.\mathrm{5}{km}/{h} \\ $$$$\left.{Q}.\mathrm{13}\right)\:\:\left(\mathrm{3}\right)\:\:\mathrm{2}{h}\:\mathrm{40}{min}\:. \\ $$

Commented by Tinkutara last updated on 23/May/17