A car travels at 5⁄7 of its actual speed and covers 42 km in 1 hr 40 min 48 sec. What is the car's actual speed (in km/h)?

When a car runs at a fraction of its actual speed, the time taken scales inversely. Here the car runs at (5⁄7) of its actual speed and takes 1 hr 40 min 48 sec to cover 42 km.

Given data

• Distance = 42 km
• Reduced speed = (5⁄7) × (actual speed v)
• Time taken at reduced speed = 1 h 40 m 48 s = 1.68 h

Step-by-step calculation
Time = Distance / Speed1.68 = 42 / [(5⁄7) v] = 42 × 7 / (5v)1.68 = 294 / (5v)5v = 294 / 1.68 = 175v = 35 km/h

Verification
Reduced speed = (5⁄7) × 35 = 25 km/hTime = 42 / 25 = 1.68 h = 1 h 40 m 48 s (matches)

Common pitfalls
Do not forget to convert 40 min 48 s entirely into hours before substituting. Mixing hours and minutes directly leads to errors.

Final Answer
35 km/h