Question

After classes on Friday, students wanted to travel to Como on a train that leaves the Lugano station at 15:55 pm. They board the 15:36 pm bus outside the school parking lot. The Collina d’Oro was full of traffic and the bus could only travel at an average speed of 20 km/h for the 2 km to the first stoplight. The bus then had to wait at the stoplight for 1 minute. After turning the corner the bus could still only average 20 km/h for the next 4 km down to the bus stop at the back of the train station. The students knew they needed to hurry and sprinted the last 300 meters from the bus stop, under the tracks and up to the train platform at an average speed of 5 m/s. Do they make it before the train leaves at exactly its scheduled time of 15:55 pm?

Answer 1

The students didn't make it before the train leaves at exactly its scheduled time of 15:55 pm.

The given parameters;

• average speed of the bus, = 20 km/h
• first distance traveled by the train, = 2 km
• time spent by the bus waiting,  = 1 min
• second average speed of the car, = 20 km/h
• second distance traveled, = 4 km
• speed of the student = 5 m/s
• distance the student covered running = 300 m

The time spent by the bus during the first motion;

$time = \frac{distance}{speed}\\\\time = \frac{2 \ km}{20 \ km/hr} \\\\time = 0.1 \ hr = 6 \min$

total time = 6 min + 1 min spent waiting = 7 min

The time spent by the bus during the second motion;

$time = \frac{4 \ km}{20 \ km/hr} \\\\time = 0.2 \ hr = 12 \min$

The time spent by the students running to cover the remaining distance;

$time = \frac{300 \ m}{5\ m/s} \\\\time = 60 \ s = 1 \min$

The total time spent by the students before getting to the train station;

t = 7 min  +  12 min + 1 min = 20 min

The minimum time the students need to make it to the train station before the train leaves;

t' = 15:55 - 15:36 = (55 - 36) = 19 min

Thus, the students didn't make it before the train leaves at exactly its scheduled time of 15:55 pm.

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