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Question Number 99366 by PengagumRahasiamu last updated on 20/Jun/20

Two buses start from a point such that one bus travelling at 80 km/h reaches its destination 2 hours before the other bus which travels at 60 km/h. However the distance travelled by the bus travelling at 60 km/h is 40 km more than that of the other bus. Find the distance travelled by the bus which is travelling at 80 km/h.

$$\mathrm{Two}\:\mathrm{buses}\:\mathrm{start}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{one}\:\mathrm{bus}\:\mathrm{travelling}\:\mathrm{at}\:\mathrm{80}\:\mathrm{km}/\mathrm{h}\:\mathrm{reaches} \\ $$$$\mathrm{its}\:\mathrm{destination}\:\mathrm{2}\:\mathrm{hours}\:\mathrm{before}\:\mathrm{the}\:\mathrm{other} \\ $$$$\mathrm{bus}\:\mathrm{which}\:\mathrm{travels}\:\mathrm{at}\:\mathrm{60}\:\mathrm{km}/\mathrm{h}.\:\mathrm{However} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{bus} \\ $$$$\mathrm{travelling}\:\mathrm{at}\:\mathrm{60}\:\mathrm{km}/\mathrm{h}\:\mathrm{is}\:\mathrm{40}\:\mathrm{km}\:\mathrm{more}\:\mathrm{than} \\ $$$$\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{bus}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{which}\:\mathrm{is}\:\mathrm{travelling} \\ $$$$\mathrm{at}\:\mathrm{80}\:\mathrm{km}/\mathrm{h}. \\ $$

Answered by MWSuSon last updated on 20/Jun/20

Distance should be 320km.

$$\mathrm{Distance}\:\mathrm{should}\:\mathrm{be}\:\mathrm{320km}. \\ $$

Answered by MWSuSon last updated on 20/Jun/20

let Bus A be the bus travelling at 80km/h, and Bus B be the bus tra− velling 60km/h. speed = ((distance)/(time)) Bus A⇒80km/h=(x/t), x is the dist− ance and t is time taken. Bus B⇒60km/h=((40km+x)/t) from Bus B, t=((40+x)/(60)), but Bus A t− ook 2hrs less to reach its destination ⇒ t−2=((x−80)/(60)) ⇒Bus A = 80=(x/((x−80)/(60)))=((60x)/(x−80)) 80x−6400=60x 20x=6400 x=((6400)/(20)) x=320km//

$$\mathrm{let}\:\mathrm{Bus}\:\mathrm{A}\:\mathrm{be}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{travelling}\:\mathrm{at}\: \\ $$$$\mathrm{80km}/\mathrm{h},\:\mathrm{and}\:\mathrm{Bus}\:\mathrm{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{tra}− \\ $$$$\mathrm{velling}\:\mathrm{60km}/\mathrm{h}. \\ $$$$\mathrm{speed}\:=\:\frac{\mathrm{distance}}{\mathrm{time}} \\ $$$$\mathrm{Bus}\:\mathrm{A}\Rightarrow\mathrm{80km}/\mathrm{h}=\frac{\mathrm{x}}{\mathrm{t}},\:\mathrm{x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{dist}− \\ $$$$\mathrm{ance}\:\mathrm{and}\:\mathrm{t}\:\mathrm{is}\:\mathrm{time}\:\mathrm{taken}. \\ $$$$\mathrm{Bus}\:\mathrm{B}\Rightarrow\mathrm{60km}/\mathrm{h}=\frac{\mathrm{40km}+\mathrm{x}}{\mathrm{t}} \\ $$$$\mathrm{from}\:\mathrm{Bus}\:\mathrm{B},\:\mathrm{t}=\frac{\mathrm{40}+\mathrm{x}}{\mathrm{60}},\:\mathrm{but}\:\mathrm{Bus}\:\mathrm{A}\:\mathrm{t}− \\ $$$$\mathrm{ook}\:\mathrm{2hrs}\:\mathrm{less}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{its}\:\mathrm{destination} \\ $$$$\Rightarrow\:\mathrm{t}−\mathrm{2}=\frac{\mathrm{x}−\mathrm{80}}{\mathrm{60}} \\ $$$$\Rightarrow\mathrm{Bus}\:\mathrm{A}\:=\:\mathrm{80}=\frac{\mathrm{x}}{\frac{\mathrm{x}−\mathrm{80}}{\mathrm{60}}}=\frac{\mathrm{60x}}{\mathrm{x}−\mathrm{80}} \\ $$$$\mathrm{80x}−\mathrm{6400}=\mathrm{60x} \\ $$$$\mathrm{20x}=\mathrm{6400} \\ $$$$\mathrm{x}=\frac{\mathrm{6400}}{\mathrm{20}} \\ $$$$\mathrm{x}=\mathrm{320km}// \\ $$

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