Two stations P and Q are 160 km apart. Two trains start simultaneously from P and Q towards each other and meet after 4 hours. If the train from P is 6 km/h faster than the other, find the speeds of both trains (in km/h).

Introduction / Context:When two trains move towards each other, the sum of their speeds equals total distance divided by meeting time. The additional given speed difference yields two linear equations in two unknowns.

Given Data / Assumptions:

• Distance = 160 km; meeting time = 4 h
• Let v_Q be the slower speed; v_P = v_Q + 6

Concept / Approach:v_P + v_Q = 160/4 = 40. With v_P = v_Q + 6, solve simultaneously.

Step-by-Step Solution:

Verification / Alternative check:Sum = 40 km/h; time = 160/40 = 4 h ✔

Why Other Options Are Wrong:

• Other pairs do not sum to 40 with a difference of 6.

Common Pitfalls:

• Assigning the +6 to the wrong train or mis-summing to 40.

Final Answer:17 km/h, 23 km/h