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Sumit travels from his home to office at 30 km/h and reaches 12 minutes late. When he increases his speed by 10 km/h he reaches 6 minutes earlier. What is the distance between his office and home?

Sumit travels from his home to office at 30 km/h and reaches 12 minutes late. When he increases his speed by 10 km/h he reaches 6 minutes earlier. What is the distance between his office and home? Correct Answer 36 km

Given:

Initial speed(S1) = 30 km/hr

New speed(S2) = 40 km/h

Concept:

When same distance is travelled with different speeds, the ratio of time taken is the reciprocal of the ratio of respective speeds.

S1/S2 = T2/T1

Formula used:

Distance travelled = Speed × time taken

Calculation:

Let the exact time to reach office = x hrs

∴ Time taken with speed 30 km/h(T1) = (x + 12) min

Time taken with speed 40 km/h(T2) = (x - 6) min

∵ T2/T1 = S1/S2

⇒ T2/T1 = 40/30

⇒ T2/T1 = 4/3

Let T1 = 4a

T2 = 3a

∴ T1 - T2 = 4a - 3a = a

∵ T1 - T2 = x + 12 - x + 6

= 18 min

∴ a = 18 min

∴ Time taken to reach office  with speed 30 km/h = 4a = 4 × 18 = 72 min = (72/60) hrs

∴ Distance between office and home = (30 km/h) × (72/60) km

= 36 km

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