A train covered a certain distance at a uniform speed. If the train ha

1.	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» 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 ⇒ xy + 5y – 3x – 15 = xy ⇒ 5y – 3x = 15 ………(i) 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 ⇒ xy – 4y + 3x – 12 = xy ⇒ 3x – 4y = 12 ………(ii) On adding (i) and (ii), we get: y = 27 On substituting y = 27 in (i), we get: 5 × 27 – 3x = 15 ⇒135 – 3x = 15 ⇒3x = 120 ⇒x = 40 ∴ Length of the journey = (xy) km = (40 × 27) km = 1080 km

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»

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

⇒ xy + 5y – 3x – 15 = xy

⇒ 5y – 3x = 15 ………(i)

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

⇒ xy – 4y + 3x – 12 = xy

⇒ 3x – 4y = 12 ………(ii)

On adding (i) and (ii), we get:

y = 27 On substituting y = 27 in (i), we get:

5 × 27 – 3x = 15

⇒135 – 3x = 15

⇒3x = 120

⇒x = 40

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