Question
Download Solution PDFA person goes to his office at the speed of 54 km/hr and reaches 18 minutes earlier. If he goes at the speed 36 km/hr, then he reaches 18 minutes late. What should be the speed to reach on the usual time?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Speed 1 = 54 km/hr → reaches 18 min early
Speed 2 = 36 km/hr → reaches 18 min late
Total time difference = 18 + 18 = 36 min = 36/60 = 3/5 hr
Formula used:
Distance = (S1 × S2 × Time Difference) / (S1 - S2)
Calculation:
⇒ Distance = (54 × 36 × 3/5) / (54 - 36)
⇒ Distance = (1944 × 3/5) / 18
⇒ Distance = (5832 / 5) / 18 = 5832 / (5 × 18) = 5832 / 90 = 64.8 km
Usual time = 64.8 / x
Also, 64.8 / 54 = 6/5 hr → 18 min early
⇒ Usual time = 6/5 + 3/10 = 15/10 = 3/2 hr
⇒ 64.8 / x = 3/2
⇒ x = 64.8 × 2 / 3 = 129.6 / 3 = 43.2 = 216/5
∴ Required speed = 216/5 km/hr
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