Sure, let's solve this step by step.

1. First, we need to convert the speed of the two persons from km/hr to m/s because the time taken by the train to overtake them is given in seconds. We know that 1 km/hr is approximately equal to 0.278 m/s. So, the speed of the first person is 4.5 km/hr * 0.278 m/s = 1.25 m/s and the speed of the second person is 5.4 km/hr * 0.278 m/s = 1.5 m/s.

2. The speed of the train relative to the first person is the distance it travels to overtake the first person divided by the time it takes to do so. The distance the train travels to overtake the first person is the distance the first person travels in 8.4 seconds plus the length of the train. Since we don't know the length of the train, we'll call it L. So, the distance the train travels is 1.25 m/s * 8.4 s + L = 10.5 m + L. The speed of the train relative to the first person is then (10.5 m + L) / 8.4 s.

3. We can do the same calculation for the second person to get that the speed of the train relative to the second person is (1.5 m/s * 8.5 s + L) / 8.5 s = 12.75 m + L / 8.5 s.

4. Since the speed of the train relative to both persons should be the same, we can set the two speeds equal to each other and solve for L. Doing so gives us L = 1.5 m.

5. Substituting L = 1.5 m back into either of the expressions for the speed of the train gives us the speed of the train relative to a person walking along the track. This is the speed of the train minus the speed of the person, so the speed of the train is the speed of the train relative to the person plus the speed of the person. Using the speed relative to the first person gives us the speed of the train as (10.5 m + 1.5 m) / 8.4 s + 1.25 m/s = 1.42 m/s + 1.25 m/s = 2.67 m/s.

6. Finally, we convert the speed of the train back to km/hr by dividing by 0.278 m/s. This gives us the speed of the train as 2.67 m/s / 0.278 m/s = 9.6 km/hr.

Question

Sure, let's solve this step by step.

1. First, we need to convert the speed of the two persons from km/hr to m/s because the time taken by the train to overtake them is given in seconds. We know that 1 km/hr is approximately equal to 0.278 m/s. So, the speed of the first person is 4.5 km/hr * 0.278 m/s = 1.25 m/s and the speed of the second person is 5.4 km/hr * 0.278 m/s = 1.5 m/s.

2. The speed of the train relative to the first person is the distance it travels to overtake the first person divided by the time it takes to do so. The distance the train travels to overtake the first person is the distance the first person travels in 8.4 seconds plus the length of the train. Since we don't know the length of the train, we'll call it L. So, the distance the train travels is 1.25 m/s * 8.4 s + L = 10.5 m + L. The speed of the train relative to the first person is then (10.5 m + L) / 8.4 s.

3. We can do the same calculation for the second person to get that the speed of the train relative to the second person is (1.5 m/s * 8.5 s + L) / 8.5 s = 12.75 m + L / 8.5 s.

4. Since the speed of the train relative to both persons should be the same, we can set the two speeds equal to each other and solve for L. Doing so gives us L = 1.5 m.

5. Substituting L = 1.5 m back into either of the expressions for the speed of the train gives us the speed of the train relative to a person walking along the track. This is the speed of the train minus the speed of the person, so the speed of the train is the speed of the train relative to the person plus the speed of the person. Using the speed relative to the first person gives us the speed of the train as (10.5 m + 1.5 m) / 8.4 s + 1.25 m/s = 1.42 m/s + 1.25 m/s = 2.67 m/s.

6. Finally, we convert the speed of the train back to km/hr by dividing by 0.278 m/s. This gives us the speed of the train as 2.67 m/s / 0.278 m/s = 9.6 km/hr.

Knowee AI · Accepted Answer

Sure, let's solve this step by step.

1. First, we need to convert the speed of the two persons from km/hr to m/s because the time taken by the train to overtake them is given in seconds. We know that 1 km/hr is approximately equal to 0.278 m/s. So, the speed of the first person is 4.5 km/hr * 0.278 m/s = 1.25 m/s and the speed of the second person is 5.4 km/hr * 0.278 m/s = 1.5 m/s.

2. The speed of the train relative to the first person is the distance it travels to overtake the first person divided by the time it takes to do so. The distance the train travels to overtake the first person is the distance the first person travels in 8.4 seconds plus the length of the train. Since we don't know the length of the train, we'll call it L. So, the distance the train travels is 1.25 m/s * 8.4 s + L = 10.5 m + L. The speed of the train relative to the first person is then (10.5 m + L) / 8.4 s.

3. We can do the same calculation for the second person to get that the speed of the train relative to the second person is (1.5 m/s * 8.5 s + L) / 8.5 s = 12.75 m + L / 8.5 s.

4. Since the speed of the train relative to both persons should be the same, we can set the two speeds equal to each other and solve for L. Doing so gives us L = 1.5 m.

5. Substituting L = 1.5 m back into either of the expressions for the speed of the train gives us the speed of the train relative to a person walking along the track. This is the speed of the train minus the speed of the person, so the speed of the train is the speed of the train relative to the person plus the speed of the person. Using the speed relative to the first person gives us the speed of the train as (10.5 m + 1.5 m) / 8.4 s + 1.25 m/s = 1.42 m/s + 1.25 m/s = 2.67 m/s.

6. Finally, we convert the speed of the train back to km/hr by dividing by 0.278 m/s. This gives us the speed of the train as 2.67 m/s / 0.278 m/s = 9.6 km/hr.

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

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