All posts by mathconfidence

February 2019 Brain Puzzler Solution

Q: A traffic light has a cycle through green, yellow, red, green, yellow, red, etc.
Red and green are each 30 seconds with a 3 second yellow inbetween.
What is the probability that while Amir is watching during a random 3 second interval  that the color changes?

9/63 = 1/7
It is a 63 second cycle.
The light changes at t=30, t = 33 and t = 63 given three three second intervals:
[27,30] and [30, 33] and [60,63] is a total of 9 seconds out of the 63 second interval



January 2019 Brain Puzzler Solution

Q: On the way to catch an international flight, Sabina drives 35 miles per hour for an hour and realizes she will be an hour late if she continues at this speed. If she increases her speed by 15 miles per hour for the remaining part of the drive she will arrive 30 minutes early. How far is her home from the airport?

A: 210 miles
She already covered 35 miles.  She has d miles left at 50 miles an hour.

Her time left to travel would be d/50 and because she will arrive an hour late vs a half hour early, there is a 1.5 hour difference between her time this faster speed and her time at the slower speed.  So the time of d/50 is 1.5 less than d/35.

We can write this as d/50 = d/35 – 1.5    OR        d/50 + 1.5 = d/35

When you solve this, you will get that the remaining distance is 175 miles plus we have to add the original 35 miles.  It would have taken Sabina 6 hours in total at 35 mph to cover the 210 miles but instead takes her only 4.5 hours — the first hour that she drove at 35 mph (35 miles) and the next 3.5 hours at 50 mph (175 miles).