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 p q \frac{p}{q} miles an hour. If p p and q q are co-prime, then find the value of ( p + q ) (p+q) .


The answer is 413.

Yash Jain by Yash Jain , 21, India

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1 solution

Yash Jain
Feb 25, 2016
  • Let the distance from San Francisco to the Golden Gate bridge be d d which is covered in time t 1 t_{1} and distance from Golden Gate Bridge to San Francisco is covered in time t 2 t_{2} .

Then according to the question,

t 1 t_{1} = d 40 \frac{d}{40} hours

t 2 t_{2} = d 25 \frac{d}{25} hours

t 1 + t 2 t_{1} + t_{2} = d 40 + d 25 \frac{d}{40} + \frac{d}{25} = 13 d 200 \frac{13d}{200} hours

Average speed for the whole trip = > S => S miles per hour

S S = T o t a l D i s t a n c e T o t a l T i m e T a k e n \frac{Total Distance}{Total Time Taken} miles per hour

S S = 2 d 13 d 200 \frac{2d}{\frac{13d}{200}} miles per hour

S S = 400 13 \frac{400}{13} miles per hour

Now we have the average speed in the rational form where 400 and 13 are co-prime.

Thus, the answer is 400 + 13 ⇒ 413 400 + 13 \Rightarrow \boxed{413}

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