In covering a distance of 80 km, Salaj takes 5 hours more than Kevin. If Salaj…

Concept

For a fixed distance, time equals distance divided by speed. If the speed doubles, the travel time becomes half of the original travel time.

When two descriptions compare both travel times with the same reference person’s time, subtracting the relations eliminates that reference time.

Application

1. Let Salaj’s original speed be s km/h and Kevin’s travel time be t hours.

2. Salaj’s original time is 80/s hours, so 80/s = t + 5.

3. At double speed, Salaj’s time is 80/(2s) = 40/s hours, so 40/s = t - 3.

4. Subtract the second equation from the first: 80/s - 40/s = (t + 5) - (t - 3), hence 40/s = 8.

5. Therefore s = 40/8 = 5 km/h.

Cross-check

1. At 5 km/h, Salaj takes 80/5 = 16 hours. At the doubled speed of 10 km/h, he takes 80/10 = 8 hours.

2. Kevin’s time is 16 - 5 = 11 hours, and the doubled-speed time is 11 - 3 = 8 hours. Both statements are satisfied, so Salaj’s original speed is 5 km/h.