A cargo train and a passenger train, which start from two stations that are 710 km apart, are traveling towards each other. The cargo train started an hour before the passenger train, and is traveling with a speed of 110 km/hour. In how many hours will the cargo train and the passenger train meet, if the passenger train is traveling at 90 km/hour?
Actually 4 hours if you count the first hour where the passenger train isn't moving.
Vc * T + Vp * (T-1) = 710.
110*T + 90*(T-1) = 710,
110T + 90T - 90 = 710,
200T = 800,
T = 4 h.
Thank you!
bal
Well, let's do some mathemagical calculations here! The cargo train travels at 110 km/hour and started an hour earlier, which means it has a head start of 110 km. The passenger train is traveling at 90 km/hour. So, when the passenger train starts, the distance between them is 710 km - 110 km = 600 km.
Now, since they are both moving towards each other, we can say that their combined speed is 110 km/hour + 90 km/hour = 200 km/hour. To find out how long it will take for them to meet, we divide the total distance between them (600 km) by their combined speed (200 km/hour).
Therefore, it will take them 600 km / 200 km/hour = 3 hours to meet. So, after 3 hours of traveling, the cargo train and the passenger train will finally meet. It's like a heartwarming train reunion!
To find out when the cargo train and the passenger train will meet, we need to determine how long it will take for them to cover the total distance between the two stations.
Let's first calculate the time it takes for the cargo train to cover the distance. Since the cargo train started an hour earlier and is traveling at a speed of 110 km/hour, we can use the formula:
Time = Distance / Speed
Time taken by the cargo train = 710 km / 110 km/hour
= 6.45 hours (rounded to two decimal places)
Next, let's determine the time it takes for the passenger train to cover the distance. The passenger train is traveling at a speed of 90 km/hour, so:
Time taken by the passenger train = Distance / Speed
= 710 km / 90 km/hour
= 7.89 hours (rounded to two decimal places)
Now, since the cargo train started one hour earlier than the passenger train, we need to subtract one hour from the time taken by the passenger train to account for the time difference. Thus:
Adjusted time taken by the passenger train = Time taken by the passenger train - Time difference
= 7.89 hours - 1 hour
= 6.89 hours (rounded to two decimal places)
Finally, we can find the time taken for the cargo train and the passenger train to meet by considering the maximum of the time taken by the cargo train and the adjusted time taken by the passenger train. In this case, the cargo train took slightly longer, so:
Time taken for the cargo train and the passenger train to meet = 6.45 hours (rounded to two decimal places)
Therefore, the cargo train and the passenger train will meet approximately 6.45 hours after the cargo train started its journey.
Since the cargo train started an hour ago it already covered 110km of distance, meaning, the distance between the two trains is exactly 600km when the passenger train takes off. One hour later, the passenger train travels 90km and the cargo train another 110km so now they are only 400km away, the pattern here is that the trains are getting 200km closer to eachother in one hour. Another hour passes and the two trains are only 200km apart, then, exactly one hour later they meet. That's a total of 3 hours.
TL;DR: They will meet in 3 hours.