Question

A road has two sets of traffic lights, which alternate between red and green. The first set is red for 15 seconds and green for 40 seconds. The second set is red for 35 seconds and green for 15 seconds. It takes a car 60 seconds to travel between the first and second set. A pedestrian sees both sets of lights change to red at the same time. How long does he have to wait until he sees a car that is just stopped by the first set turning red which will go on to be just stopped by the second set turning red?

Answer 1

Answer:

275 seconds, or 4 min 35 s

Step-by-step explanation:

The first set is red for 15 seconds and green for 40 seconds, so it repeats the cycle every 55 seconds.

The second set is red for 35 seconds and green for 15 seconds, so it repeats the cycle every 50 seconds.

A car will stop at the first set, wait 15 seconds, then drive for 60 seconds to the second set, which will just turn red.  So we need to find how many cycles it takes for the beginning of the two sets to be 75 seconds apart.

If x is the number of cycles of the first set, and y is the number of cycles of the second set, then:

55x + 75 = 50y

y = 1.1x + 1.5

y must be an integer, so we need to find an integer value of x such that 1.1x ends in 0.5.  For example, x = 5.

y = 1.1(5) + 1.5

y = 5.5 + 1.5

y = 7

If we wait for the first set to cycle 5 times, the beginning of the 6th cycle will be 75 seconds before the beginning of the second set's 8th cycle.  So the pedestrian must wait 5 × 55 = 275 seconds, or 4 min 35 s.