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a car travels 160 km is the same time that a truck travels 120 km, if the speed of the car is 12 km per hour faster than the speed of the truck.find the both speed ?

Sagot :

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[tex]Velocity= \frac{distance}{time} \\ Time~is~the~same \\ V_{car}= \frac{160}{t} ----\ \textgreater \ t= \frac{160}{V_{car}} --equation1 \\ V_{truck}= \frac{120}{t} ----\ \textgreater \ t= \frac{120}{V_{truck}} --equation2 \\ Equate~equations~1~and~2 \\ \frac{160}{V_{car}} = \frac{120}{V_{truck}} \\ \\ 160V_{truck}=120V_{car} \\ \frac{4}{3} V_{truck} = V_{car} --equation 3 \\ \\ Given~that~the~speed~of~the~car~is~ 12km/hr~faster~than~the~truck: \\ V_{car} = V_{truck}+12 ---equation4\\ Substitute~equation~3~to~equation~4 \\ [/tex][tex] \frac{4}{3} V_{truck} = V_{truck} + 12 \\ (\frac{4}{3}V_{truck} = V_{truck} + 12) (3) \\ 4V_{truck} = 3V_{truck} + 36 \\ 4V_{truck} - 3V_{truck} = 36 \\ V_{truck} = 36km/hr \\ Substitute~V_{truck}=36km/nr~to~equation~4 \\ V_{car}=V_{truck}+12 \\ V_{car} = 36 + 12 \\ V_{car} = 48km/hr[/tex]
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