Over the Golden Gate

Algebra Level 2

While in San Francisco some time back, I hired a car to drive over the Golden Gate bridge. I started in the afternoon when there was no rush. So I could drive at a speed of 40 miles an hour. While returning, however, I got caught in the traffic rush and could only manage to drive at a speed of 25 miles an hour. The average speed for the round trip can be expressed as \(\frac{p}{q}\) miles an hour. If \(p\) and \(q\) are co-prime, then find the value of \((p+q)\).

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