Question

Carmella and Carmen simultaneously left the city and drove 120 km to a nearby town. Carmella drove at a speed that was 20 km/hr faster than Carmen. If Carmella arrived in the nearby town 1 hour before Carmen, find the speed that each of them drove.

Answer 1

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Speed of Carmen = 40km/h

and speed of Carmella = 60km/h

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

`\sf Time= (distance)/(speed)`

Let the time taken by Carmen be T1

and Carmella be T2

`\sf So \: T_1 = (120)/(x) \: and \: T_2 = (120)/(x + 20)`

As there is 1 hour difference so

`\sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies (120)/(x ) - (120)/(x + 20) = 1 \\ \\ \\ \sf \implies (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}}`

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