Question

Town P and Town Q are 80 km apart. A train travels from P to Q at an average speed of 120 km/h, waits, and travels from Q back to P at an average speed of 110 km/h. If the average speed of the train for the whole journey is 105 km/h, how long did it wait at Q? Give your answer in minutes and seconds.​

Answer 1

7 minutes 48 seconds.

Explanation:

Average speed for the whole journey is

distance / time, so

105 = (2*80)/ (t + t2)

where t is the time when it is moving and t2 is the time it stays at town Q.

Time for journey P to Q

= distance / speed

= 80 /120

= 2/3 hours,

Time for journey Q to P

= 80/110

= 8/11 hours

So t = 2/3 + 8/11

= 46/33 hours.

- and substituting in the equation for the whole journey:

160 / (46/33 + t2) = 105

105*46/33 + 105*t2 = 160

105 t2 = 160 - (105*46)/33

= 160 - 146.364

= 13.636

t2 = 13.636/105 = 0.1299 hours.

= 7 minutes 48 seconds.