Question 1

A bus travels from City A to City B at a speed of 60 km/h. On the return journey, it travels at 40 km/h. If the distance between the two cities is 120 km, what is the average speed of the bus for the entire journey (both ways)?

Accepted Answer

Step 1: Calculate time taken from A to B: Time = Distance/Speed = 120/60 = 2 hours. Step 2: Calculate time taken from B to A: Time = 120/40 = 3 hours. Step 3: Total distance covered = 120 + 120 = 240 km. Step 4: Total time taken = 2 + 3 = 5 hours. Step 5: Average speed = Total distance/Total time = 240/5 = 48 km/h. Therefore, the average speed is 48 km/h.

Question 2

A boat takes 8 hours to travel 96 km downstream and 12 hours to travel the same distance upstream. Find the speed of the boat in still water.

Accepted Answer

Step 1: Let speed of boat in still water = b km/h and speed of stream = s km/h.

Step 2: Downstream speed = b + s, Upstream speed = b - s.

Step 3: From downstream: Distance = Speed × Time → 96 = (b + s) × 8 → b + s = 12 km/h.

Step 4: From upstream: 96 = (b - s) × 12 → b - s = 8 km/h.

Step 5: Adding both equations: (b + s) + (b - s) = 12 + 8 → 2b = 20 → b = 10 km/h.

Step 6: Subtracting: (b + s) - (b - s) = 12 - 8 → 2s = 4 → s = 2 km/h.

Verification: Downstream = 10 + 2 = 12 km/h; Time = 96/12 = 8 hours ✓. Upstream = 10 - 2 = 8 km/h; Time = 96/8 = 12 hours ✓.

Therefore, the speed of the boat in still water is 10 km/h.

Question 3

Two trains start simultaneously from stations A and B, which are 450 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 90 km/h. After how much time will they meet, and at what distance from station A?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds. Relative speed = 60 + 90 = 150 km/h. Step 2: Time to meet = Total distance / Relative speed = 450 / 150 = 3 hours. Step 3: Distance of meeting point from A = Speed of Train X × Time = 60 × 3 = 180 km. Step 4: Verify: Distance from B = 90 × 3 = 270 km. Total = 180 + 270 = 450 km ✓. Therefore, trains meet after 3 hours at a distance of 180 km from station A.

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