Question

A train runs at a speed of 40:lkm/hr between 2 cities P and Q. ]t takes 5 stops in between and the
stopping time for 5 stops follows the pattern of x, 2x, 3x, 2x, x minutes. If the train takes exactly
1 hr to travell from P to Q and the lo gest stopp·ng time was 6 min.
Find the distance between P and Q (in km).

Answer 1

Answer:

900km

Step-by-step explanation:

At the time of meeting, let the distance travelled by Q, the second train be x km

Then, distance covered by first train =(x+100)km

Thus,

40

x

=

50

x+100

=>5x=4x+400

=>x=400

Thus, distance between P and Q =(x+x+100)=(400+400+100)=900km

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Answer 2

Given: Speed of the train = 40 km/hr

           Number of stops = 5 with intervals of x, 2x, 3x, 2x, x minutes

           Longest stopping time = 6 min

           Total time taken to travel = 1 hr

To find: The distance between P and Q

Solution: From the pattern of stopping time, we can say that longest time would the one with 3x minutes.

Hence according to the question,

3x = 6

⇒ x = 2

Therefore, the time intervals of x, 2x, 3x, 2x, x minutes are equal to:

2 minutes, 4 minutes, 6 minutes, 4 minutes and 2 minutes.

Thus, the total interval time = (2 + 4 + 6 + 4 + 2) minutes

                                              = 18 minutes

So the remaining time when the train was travelling = (60 - 18) minutes

                                                                                       = 42 minutes

                                                                                       = 42/60 hr

                                                                                       = 7/10 hr

Therefore, the distance between P and Q = speed × time

                                                                      = 40 km/hr × 7/10 hr

                                                                      = 28 km

Answer: 28 km