Question

Lee was riding his bike. after travelling the distance of 30 km, he sensed 3 unusual sound from the engine so he reduced his speed to 3/4th of the initial speed and reached the destination 45 min late. had he sensed the sound 12 km farther, he would have reached the destination 30 mm late. find the total distance of the journey.

Answer 1

Let x be the initial speed.

Let the total distance be S

The new speed = 3/4x

Remaining distance = S - 30

Now :

(S - 30) / (3/4x)  - S/x = 3/4

(S - 30)x - S(3/4x) = 3/4(3/4x)x

Sx - 30x - 3/4Sx = 9/16x²

4Sx - 120x - 3Sx = 9/16x²

64Sx - 1920x - 48Sx = 36x²

16Sx - 1920x = 36x²

Dividing by x

16S - 1920 = 36x

16S - 36x = 1920........ 1)

(S - 42) / (3/4x) - S/x = 1/2

(S - 42)x - S(3/4x) = 1/2(3/4x)x

Sx - 42x - 3/4Sx = 3/8x²

4Sx - 168x - 3Sx = 12/8x²

32Sx - 1344x - 24Sx = 12x²

8Sx - 1344x = 12x²

Dividing by x:

8S - 1344 = 12x

8S - 12x = 1344.. ......... 2)

Solving simultaneously.

We multiply eqn 2 by 2 then subtract 1 from it

16S - 24x = 2688

12x = 768

x = 64

Substitute this in 1.

16S - 36 × 64 = 1920

16S = 1920 + 2304

16S = 4224

S = 4224/16

S = 264 Km

Answer 2

Answer:

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