Question

A train covers a distance of 480km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. Find the original speed of the train.​

Answer 1

Answer:

Uniform speed=480km

speed had been less=8km/hr

1. therefore, 480/8
2. =60
3. Hour will increase to cover the distance= 3+60
4. = 63hr
5. Change it into units.As we all know SI units.
6. 480km= 1km = 1000m.
7. 480*1000 = 480000m.
8. 63 hr = 1hr = 3600sec.
9. =63*3600
10. 2226800sec.
11. According to question = Speed= Distance/Time
12. n= 480000/226800
13. n= 2.11m/s this is original speed of train

Hope it will help you

Answer 2

$\huge\boxed{\sf{†Solution†}}$

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

Distance covered by the train = 480 km.

★ Time taken by the train to cover the distance

of 480km = 480/x hrs.

Now, According to the given condition,

$\ \large\mathrm{ \frac{480}{x - 8} - \frac{480}{x} = 3 }$

$\mathrm{\implies \: 480\large[ \frac{1}{x - 8} - \frac{1}{x} \large] = 3}$

$\large\mathrm{\implies \frac{x - x + 8}{(x - 8) \times x} = \frac{3}{480} }$

$\large\mathrm{\implies \frac{8}{x^{2} - 8x } = \frac{1}{160} }$

$\mathrm{\implies {x}^{2} - 8x - 1280 = 0}$

$\mathrm{\implies \: {x}^{2} - 40x + 32x - 1280 = 0}$

$\mathrm{\implies \: x(x - 40) + 32(x - 40) = 0}$

$\mathrm{\implies \: ( x - 40)(x + 32) = 0}$

$\mathrm{\implies \: x - 40 = 0 \: or \: x + 32 = 0}$

$\mathrm{\therefore \: x = 40 \: or \: x = - 32}$

Speed cannot be in –ve,

Hence, Speed of the train is 40km/hr

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