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Speed and Distance Example

Motorcycle Problems Solution

Solution to Motorcycle Problems

1. When and where do the two motorcycles meet if they start simultaneously facing each other?

Given:

  • Initial distance between A and B: 2600 m
  • Speed of motorcycle A: 12 m/s
  • Speed of motorcycle B: 8 m/s

Solution:

Since they are moving towards each other, their combined (relative) speed is:

Relative speed = 12 + 8 = 20 m/s

Time taken to meet:

Time (t) = Distance / Relative speed = 2600 / 20 = 130 seconds

Distance traveled by A until they meet:

Distance by A = Speed of A × Time = 12 × 130 = 1560 m

Answer: They meet after 130 seconds, 1560 meters from A’s starting point.

2. When and where do the two motorcycles meet if A departs 10 seconds earlier?

Solution:

In the first 10 seconds, A travels:

Distance = 12 × 10 = 120 m

New distance between A and B = 2600 - 120 = 2480 m.

Time to meet with a relative speed of 20 m/s:

Time (t) = 2480 / 20 = 124 seconds

Total time from when A starts:

Total Time = 124 + 10 = 134 seconds

Distance traveled by A:

Distance by A = 12 × 134 = 1608 m

Answer: They meet after 134 seconds, 1608 meters from A’s starting point.

3. When and where does motorcycle A overtake motorcycle B if they start simultaneously in the same direction?

Solution:

Relative speed (A moving faster than B):

Relative Speed = 12 - 8 = 4 m/s

Time taken for A to overtake B:

Time (t) = 2600 / 4 = 650 seconds

Distance traveled by A:

Distance by A = 12 × 650 = 7800 m

Answer: Motorcycle A overtakes B after 650 seconds, 7800 meters from A’s starting point.

4. When and where does motorcycle A overtake motorcycle B if A departs 2 seconds earlier?

Solution:

In the first 2 seconds, A travels:

Distance = 12 × 2 = 24 m

New distance between A and B = 2600 - 24 = 2576 m.

Time taken to overtake with a relative speed of 4 m/s:

Time (t) = 2576 / 4 = 644 seconds

Total time from A's start:

Total Time = 644 + 2 = 646 seconds

Distance traveled by A:

Distance by A = 12 × 646 = 7752 m

Answer: Motorcycle A overtakes B after 646 seconds, 7752 meters from A’s starting point.

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