Question

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A train covered a certain distance at a uniform speed. If the train had been 5 kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.​

Answer 1

Step-by-step explanation:

Hey!!

Great Question

❒ Given :-

A train covered a certain distance at a uniform speed. If the train had been 5 kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey ?

❒ To Find:-

Find the length of the journey ?

❒ Solution :-

Let the original speed be x kmph and let the time taken to complete the journey be y hours.

∴ Length of the whole journey = (xy) km

Case I:

When the speed is (x + 5) kmph and the time taken is (y – 3) hrs:

Total journey = (x + 5) (y – 3) km .

• ⇒ (x + 5) (y – 3) = xy
• ⇒ (x + 5) (y – 3) = xy ⇒ xy + 5y – 3x – 15 = xy
• ⇒ (x + 5) (y – 3) = xy ⇒ xy + 5y – 3x – 15 = xy ⇒ 5y – 3x = 15

Case II:

When the speed is (x – 4) kmph and the time taken is (y + 3) hrs:

Total journey = (x – 4) (y + 3) km .

• ⇒ (x – 4) (y + 3) = xy
• ⇒ (x – 4) (y + 3) = xy ⇒ xy – 4y + 3x – 12 = xy
• ⇒ (x – 4) (y + 3) = xy ⇒ xy – 4y + 3x – 12 = xy⇒ 3x – 4y = 12

• ↳ On adding (i) and (ii), we get: y = 27 On substituting y = 27 in (i), we get = 5×27 – 3x = 15
• ⇒ 135 – 3x = 15
• ⇒ 135 – 3x = 15 ⇒ 3x = 120
• ⇒ 135 – 3x = 15 ⇒ 3x = 120 ⇒x = 40

∴ Length of the journey = (xy) km = (40 × 27) km = 1080 km

Hence , Your Answer Is = 1080 km .

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Answer 2

Answer:

Your answer is on the above attachment.

Step-by-step explanation:

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