Question

b) If the speed of a car is increased by 12 km/h, it takes 40 minutes less to cover a
distance of 240 km. Find the original speed of the car.


Solution:
The distance covered by the car = 240 km

Let's consider,

"S km/hr" → represents the original speed of the car

"(S + 12) km/hr" → represents the increased new speed of the car

We know,

\boxed{\bold{Time = \frac{Distance }{Speed} }}
Time=
Speed
Distance
​

​


According to the question and the formula above, we can form an equation as:

\frac{240}{S} - \frac{240}{S+ 12} = \frac{40}{60}
S
240
​
−
S+12
240
​
=
60
40
​


\implies 240 [\frac{1}{S} - \frac{1 }{S + 12} ] = \frac{2}{3}⟹240[
S
1
​
−
S+12
1
​
]=
3
2
​


\implies \frac{1}{S} - \frac{1 }{S + 12} = \frac{1}{360}⟹
S
1
​
−
S+12
1
​
=
360
1
​


\implies \frac{S+ 12 - S}{S(S+12)} = \frac{1}{360}⟹
S(S+12)
S+12−S
​
=
360
1
​


\implies \frac{ 12 }{S(S+12)} = \frac{1}{360}⟹
S(S+12)
12
​
=
360
1
​


\implies S^2 + 12S = 4320⟹S
2
+12S=4320

\implies S^2 + 12S - 4320 = 0⟹S
2
+12S−4320=0

\implies S^2 + 72S - 60S - 4320 = 0⟹S
2
+72S−60S−4320=0

\implies S(S + 72) - 60(S + 72) = 0⟹S(S+72)−60(S+72)=0

(S + 72) (S - 60) =

0⟹(S+72)(S−60)=0

S = -72 60

⟹S=−72or60

since speed cannot be negative, so taking the positive value of the speed

⟹S=60km/hr

Thus, the original speed of the car is → 60 km/hr.​

Answer 1

Answer:

this answer is ..ok but too long ..Do it inverse variation ..Then it will be shorter

Answer 2

Answer:

Hey are you mad why are you doing this long method do this in short