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3 years from now will be 360. We would like I THU

(iv) A train travels a distance of 480 km at a uniform speed. If the speed

Question

3 years from now will be 360. We would like I THU

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been

8 km/h less, then it would have taken 3 hours more to cover the same distance. We

need to find the speed of the train. a quadratic equation for this???

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Mathematics
1 year
2021-07-15T15:22:51+00:00
2021-07-15T15:22:51+00:00 2 Answers
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## Answers ( )

Answer

Let the speed of the train be x km/hr. Then

Time taken to travel a distance of 480km=

x

480

hr

Time taken by the train to travel a distance of 480km with the speed (x−8)km/hr=

x−8

480

hr

It is given that if the speed had been 8km/hr less, then the train would have taken 3 hours more to cover the same distance

∴

x−8

480

=

x

480

+3

⇒

x−8

480

−

x

480

=3⇒

x(x−8)

480(x−x+8)

=3⇒

x(x−8)

480×8

=3

⇒3x(x−8)=480×8⇒x(x−8)=160×8⇒x

2

−8x−1280=0

This is the required quadratic equation.

: ANSWERThe speed of train is = 40 km /hr

:GIVENDistance covered = 480 km

if the speed has been 8 km / hr less

:FINDSpeed of the train

:SOLUTIONLet the normal speed be x km \hr

We know that

Time = Distance/ speed

[tex]\mapsto[/tex] Cross multiplying

[tex]\mapsto[/tex] 480x – 480x + 3840=3(x2- 8x)

Factories by splitting the middle term

Here speed can’t be negative

So, the train speed is 40 km /hr