Respuesta :
[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]
Speed of Carmen = 40km/h
and speed of Carmella = 60km/h
Step-by-step explanation:
Let the speed of Carmen = x km/h
Carmella speed will be (x + 20)km/h
Distance = 120 km
Time between Carmen and Carmella = 1 hour
[tex] \sf Time= \frac{distance}{speed} [/tex]
Let the time taken by Carmen be T1
and Carmella be T2
[tex] \sf So \: T_1 = \frac{120}{x} \: and \: T_2 = \frac{120}{x + 20} [/tex]
As there is 1 hour difference so
[tex] \sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies \frac{120}{x } - \frac{120}{x + 20} = 1 \\ \\ \\ \sf \implies \frac{120(x + 20) - 120x}{x(x + 20)} = 1 \\ \\ \\ \sf \implies 120x + 2400 - 120x = {x}^{2} + 20x \\ \\ \\ \sf \implies 2400 = {x}^{2} + 20x \\ \\ \\ \sf \implies 0 = {x}^{2} + 20x - 2400 \\ \\ \\ \sf \implies 0 = {x}^{2} + 60x - 40x - 2400 \\ \\ \\ \sf \implies0 = x(x + 60) - 40(x + 60) \\ \\ \\ \sf \implies 0 = (x + 60)(x - 40) \\ \\ \\ \sf \implies \red{\boxed{x = 40km}}[/tex]
We have not considered 60 as it will become negative value and negative value is not possible in distance
Speed of Carmen = 40km/h
Speed of Carmella = 40 + 20 = 60km/h
