The speeds of two cars are in the ratio 5 : 3. If they cover the same total distance, and the slower car takes 2.5 hours, how much time does the faster car take?
Explanation:
Ratio of speeds = 5:3, so ratio of times taken = 3:5. The slower car corresponds to 5 parts = 2.5 hours => 1 part = 0.5 hours. Time for the faster car = 3 parts = 3 * 0.5 = 1.5 hours.
A car covered a distance of 300 km at a uniform speed. If the baseline speed is lowered by 10 km/h, the trip duration spikes by 1 hour. Find the original speed.
Explanation:
Let original speed be s. 300 / (s - 10) - 300 / s = 1 => 300(10) = s(s - 10) => 3000 = s(s - 10). Solving s^2 - 10s - 3000 = 0 yields (s - 60)(s + 50) = 0. Since speed must be positive, s = 60 km/h.
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