A car takes p minutes to travel a distance of 350 km with an average speed of u km/hr. Another car takes q minutes to travel the same distance with an average speed of v km/hr. If u-v=5 and q-p=140, then what is the value of u?

Explanation

Time difference in hours is \frac{q}{60} - \frac{p}{60} = \frac{140}{60} = \frac{7}{3}. Thus, \frac{350}{v} - \frac{350}{u} = \frac{7}{3}. Substituting v = u - 5 yields \frac{350 \times 5}{u(u-5)} = \frac{7}{3}, which simplifies to u(u-5) = 750. Solving the quadratic gives u=30.

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